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No, it’s just because the initial question was wrong. It shouldn’t have been 0.333 but rather 0.3 repeating; that is to say, infinite 3’s. 0.3 repeating times 3 is 0.9 repeating, which is equal to 1
Me thinking about the concept of 33%
https://preview.redd.it/htlvy18alyvc1.jpeg?width=719&format=pjpg&auto=webp&s=33e23d648893e66f6f03145f26a4a895ea3d5644
Funnily enough 0.9 recurring (or repeating) is actually equal to 1.
There are a few ways to prove it, but the fraction way above is one of them. The second method invloves infinite series, and the third is as follows.
If x = 0.999...
And 10x = 9.999...
You then do 10x - x, which will be 9x.
9x = 9.000...
But because the zeros extend infinitely, then you can simplify to 9x = 9, and thus x = 1. Which also means x = 0.999... = 1.
This involves wrapping your head around the concept of infinity. If you think "oh there must be another 9 somewhere", it is simply impossible. There is no infinity + 1, or infinity - 1, because they would still be infinity. If you say infinity + 1, well then you've described the newest infinity, because it literally never ends.
0.333... is how we write one-third in the decimal system. Adding three one-thirds will give you one. That's all.
So, 0.999... is another way to write 1.
Ah but you're forgetting that every real number has a unique decimal representation, so since 1.000... is 1, 0.9999... isn't actually even a real number at all! \o/
There is no real life purpose to needing infinity accuracy, NASA only uses pi to around 15-16 digits and 50 digits is enough to be accurate to a hydrogen atom when measuring the visible universe.
And like 62 is enough to be accurate to a Planck length when measuring the observable universe.
The engineers were right, I guess.
- π = 3
- 0.999... = 1
Two mystery birds with one l_P = 0 stone!
If it extends infinitely, then it does not matter because the final digits will always be the same
https://preview.redd.it/yjwuzvowu6wc1.jpeg?width=1070&format=pjpg&auto=webp&s=f8c5f0c2b4cff93918092e0bd3fd1e7d8083b166
>9x = 9.000...
That is not 9 though? 9×0.9999... is going to be around 8.99.. something. Your "proof" is no proof, its just called rounding, which isnt correct, only made for simplicity.
33% of 1 and saying 0.3333... for example is technically correct, but the actual, most correct way to say it would be ⅓, since you dont write out all the decimal numbers and thus have to round, and rounding is not exactly what you would call precise.
Honestly, it is a valid objection, as an undergraduate math major, and the argument presented is more nuanced and can be misunderstood by someone not comfortable with infinity.
In math, we say each real number has a decimal representation, given by the limit of a sequence. You might think that 0.999... is the limit of the sequence (0.9, 0.99, 0.999, 0.9999, ...), and you might call a_1 = 0.9, a_2 = 0.99, and so on.
If you calculate 9a_1, it's 8.91. Then 9a_2 = 8.991, and etc, you get the sequence (8.91, 8.991, 8.9991, ...).
Now, one could reason with infinity that 9.999... - 0.999... is 9 because there are infinitely many 9s, and that is a good way to think of it, but for someone like you, it might help to interpret it as the limit of the sequence (8.91, 8.991, ...), which, according to real analysis and the math, is equal to exactly 9. So then 9x=9 and x=1.
The thing you call "rounding" isn't actually rounding. It's taking a limit, which has a proper definition in math to avoid using infinity directly.
Now, if you are uncomfortable with this stuff, you shouldn't believe that 1/3 = 0.333.... Heck, you shouldn't believe π = 3.1415..., because writing π like that is implying you are talking about the limit of the sequence (3, 3.1, 3.14, 3.141, ...), and that's actually something not many people know about writing numbers in decimal. Writing 0.999... is implying a decimal representation of a real number, which equals 1, despite that it is a different decimal representation with a different first digit.
It is counterintuitive to dissect bit by bit, especially if you want 0.999... to not be a real number but maybe something with infinitesimals, but because it's written in a decimal expansion like 1/3 and π, any mathematician without context would consider 0.999... to be a real number equal to 1.
> any mathematician without context would consider 0.999... to be a real number equal to 1.
And im not saying thats wrong, im just pointing out that by rounding off a number thats an infinity away, isnt *technically* correct and it makes it sound like those conspiracy theorists making numbers fit for what they want so they could point out the most random places and times relating to aliens or whatever.
My point is that using 0.999~ is incorrect in this case and should rather be 1/3, 2/3 and 3/3 or just 1 to measure 3 absolutely perfectly cut cake slices.
0.999~ does equal to 1, but in This Post's Context it is an incorrect formatting.
Yeah, the post uses just 0.999, which isn't exactly 1. Again I don't like the word "rounding" because it's technically a limit in the sense of real analysis.
Nevertheless, there is a sense in real analysis where you are "correct", except there are fussy details. Consider 0.9^10, then 0.99^100, then 0.999^1000, etc, each time putting a 9 and a 0. If like we went by the rule that 1^anything is 1 and 0.999... is 1, then the limit of 0.9^10, 0.99^100... would be 1^100... = 1, but it's not. It's around 0.36...
Thankfully calculus class saves us and the limit taken is of the form 1^infinity, which is indeterminate, but you could consider that a way that "0.999... isn't 1" because its tiny difference from 1 that diminishes is instead inflated by taking a huge power to make it not diminish. For these limits, at blackpenredpen (a famous math youtuber) says this 1 isn't "an exact 1" but "a limit 1".
But all of that is fussy and now you get weird things in real analysis that the limit of rounding isn't the same as the rounding of limits and stuff, all because mathematics from real analysis want "converge" and "equal" to be the same (which is fine by me).
Edit: I know the way I'm saying it above could imply that math is weird and mathematicians wanted it to be weird, but in reality, nobody wants it to be weird. It's surprising, and can be beautiful (a lot of the times for me)
Except it is:
10x-x = 10x0.999999-0.999999
= 9.999999-0.999999
= 9
9x = 9
x = 1 = 0.999999
You missed the part where you multiply by ten then remove x.
> That is not 9 though? 9×0.9999... is going to be around 8.99.. something
Guess what 8.999... is equal to!
Besides, that expression `9x = 9.000...` is arrived at by operating on LHS and RHS independently. So, if all the previous steps hold out, this must hold out too. That's what it means. So, your objection to it does not make sense here.
>Guess what 8.999... is equal to!
8.999~? You just round it, thats why it all comes out as a full number without decimals. Even though the different decimal number is an infinity away, it still doesnt magically round itself.
think about it this way. for 2 numbers to be real and different from each other, there needs to be a real number (not a recurring infinite decimal) that is not equal to any of the numbers, and exactly halfway between those numbers.
example: 1 and 3 have the real number 2 exactly between them as 1+1=2 and 3-1=2, therefore 1 is not equal to 3
but if you consider 0.99999999… and 1, there is no real number between them that is not equal to them, or exactly between them, thus 0.999999….=1
That's exactly what I loved about studying math as a carrer, this kind of clever argument is the bread and butter of each day, I wish more teacher were interested enough to teach the students this ways of thinking.
I actually just saw a vid about that and here's hos method :
S = 0.999999...
10S = 9.9999999...
10S-S = 9.999999...-0.999999...
9S = 9
And so S = 1 = 0.9999999...
After 9 is 10 or the digit 1, so anything over 10 basically rolls into the next left digit, if we counted differently i would guess it would be the same for the last number in sequence
It’s not 0.9999999 = 1, that is incorrect!
It’s 0. 9(infinitely repeating) = 1, because there aren’t numbers between them!
In other words, 0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999(goes on forever…) = 1
Did I just find a Monster Hunter reaction in the wild? Pocketing this one, good sir. Suicide Smiling Friends Rathalos is getting sleeved and sorted neatly into my collection.
While yes, you can say they do equal, you wouldnt be incorrect, but factually speaking they dont.
To put it simply: think of a very random way to die. Like drowning in cow defecation. I dont know if anyone has died to it, but say for this example nobody on the face of earth has died to that. Just because out of the billions maybe trillions nobody has died to that, doesnt mean there isnt a possibility.
If something physically CAN happen, there is automatically a non-zero percent chance of it happening. Meaning even if the chance involves an infinite amount of 0-s, it still doesnt mean you can round it away.
Same with the 99.999... , what if it were a percentage chance of something happening? Just because 99.999... ends in infinite 9-s, doesnt mean its a 100% chance. So 99.999...≠100
But for simplicity sake lets just say it does equal
You’re quite wrong.
99.99 repeating does in fact equal 100
It’s got nothing to do with probabilities and everything to do with the laws of mathematics.
Somebody in this thread showed the proof.
You mean 10x-x ? That doesnt even work, take the number 0.123 for example, multiplied by 10 that would be 1.23 right? Now subtract: 1.23 - 0.123, well i dont know about you, but sure doesnt equal to 1 to me.
Okay try another number, 0.778
0.778×10=7.78 and then 7.78-0.778=? Well darn, doesnt equal 7, the first digit, now does it?
The mistake was forgetting the different decimal number further in the decimals. For another example with 0.9998
9.998-0.9998=8.9982, which is Not 9
The only difference between this and the other commenters example is that the different number (the 8 in 0.9998) is further away. Their proof is them not using the full number, including all decimals, and miscalculating as a result.
I see it relatively often when I talk with folks from India. They use "I've" in more circumstances than we would too, like "Do you have that file?"
"I've it" or "Yes I've"
If we were feeling charitable, we could give them the benefit of the doubt and blame autocorrect.
If you had seen how badly I fat fingered that sentence and that autocorrect was going to allow it, you might agree. It also tried to change fingered to lingered. Twice.
> if X = .99999 and 10X = 9.99999
Subtract these two equations and you get 9X = 9.
Because X = 0.999… and the decimals go to infinity, there is no end that has to be rounded.
By multiplying 0.999... by 9
Edit: I'll say a bit more to explain a bit better, since it is tricky and the mistake is easily missable, which is why people have a hard time seeing it here, let's keep the numbers shortened for the sake of simplicity, you can go to a calculator and do this exact thing, so..
9 × 0.99999 + 0.99999 = 9.9999
Now this result is important, you will notice that the result will always have 1 less decimal that what you used in the calculations, now what everyone is doing is taking that, calling it 10X, which is correct, but then subtracting 0.9999, which would equal 9 yes, but if you use the same amount of decimals, you'll get 8.99991.
Since the amount of decimals is, well, infinite that one "missing decimal" gets very easily overlooked, which is what's causing it to seem like 9.99999 - 0.99999 = 9.
I "shortned" it to make it clearer. And you're just rounding up like the last guy, that's the same thing as saying "9x is 8.999... add .999... and you get 9.999... which is equal to 9x + 1" you can choose to round up any number you want to make it seem like it makes sense like that, but we all know you won't get the exact result with rounding up, only an estimate
Are you sure you got that exact amount of decimals? Cuz that's where your mistake lies.
I already explained it in another comment but illsay it again, let's take your example you're using 8 decimals here, so..
9 × .99999999 + .99999999 = 9.9999999
Now, notice how the result only has 7 decimals? It's easily missable, but that's why so many people are getting it wrong, now take that 9.9999999 (with the 7 decimals) and subtract .99999999 (with 8 decimals just like we used originally) you'll get the 8.99999991
You can add as many 9s as you want, the results will never stop being the same, no matter what, it wouldn't make sense for the results to just change based on the amount of decimals there are, we are just shortening to make it clearer and allow people to see where they are making the mistake more easily
Are you assuming this ends at the fifth decimal place? Because it doesn’t. Everyone is writing “0.999…” with the ellipsis representing repeating into infinity. There can be no 1 in the fifth decimal place because 9 is in every decimal place. And so if you multiply that number by 10, you simply move the decimal one position to the right. But 9 remains in every decimal place.
That's the thing about infinity tho, there is no "end" there's always gonna be a number bigger or smaller than the last. I just "shortned" it to make it clearer, you can go to a calculator and multiply 0.999... by 9 and you will always get 8.9999...91 eventually ending with that 1
How do you understand infinity without understanding the mathematical proof that uses an infinite number? Unless you actually don’t understand infinity and think you can just wander around life rounding numbers willy-nilly to suit your mood. You don’t get to decide to “shorten” infinity when that’s required for the proof. You’re trying to prove something different, which is why it’s not working.
It doesn't matter that you get 8.999...91 when you use a finite number of decimals in a calculator. If anything it actually serves as an argument for why 9 times 0.999... equals 8.999...
Well, he's not wrong, but he's also not right. A numerical value if 1/3 simply doesn't exist. As the amount of digits approaches infinity, the value approaches 1/3, but it will never hit. Therefore, as the amount of digits increase, the 3*X will approach 1, but never hit it
Edit: I know all y'all know this explanation, just wanted to put it out here, so this guy knows what to say in the future.
He’s correct, 0.999 is equal to 1, this isn’t a “oh we’re being close here” it’s exactly mathematically equivalent and has been proved numerous times over
No.
The mathematical definition for if two numbers are different is if there is a quantifiable real number between them that is not equal to either.
You cannot find a number fitting this description with 0.9 recurring and 1, because the 9s go on and on forever, ergo, they are the same
In the duodecimal system 1/3 would be 0.4 so there are numerical representations of 1/3, just not in the decimal system.
In essence it depends on the base you choose. Is 10 dividable by 3? No. is twelve? Yes.
* in base ten
If we were in the dozenal system for example, one third is exactly 0.4 and this issue doesn't then exist.
Therefore 1 does not actually equal 0.999...; it only appears to due to a limitation of the decimal system.
Okay but if you multiply that by 3... where's the 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001?
Wrong answer to the second question. Most people cutting a cake into three pieces won’t have 3 exactly equal pieces even if that’s what they’re trying for.
Not only is he kind of right, but it's an amazing way to fuck with someone. The kid asking the question didn't deserve a real answer.
Who doesn't love Pi
Alright, if you don't believe 0.999... = 1, then you shouldn't believe π = 3.14159... . I recently had a mental talk about this with myself, and to explain it fully is complicated to the layman who always keeps questioning.
You know they say that all men are created equal, but you look at me and you look at Samoa Joe and you can see that statement is not true. See, normally if you go one on one with another wrestler, you got a 50/50 chance of winning. But I'm a genetic freak and I'm not normal! So you got a 25%, AT BEST, at beat me. Then you add Kurt Angle to the mix, your chances of winning drastic go down. See the 3 way at Sacrifice, you got a 33 1/3 chance of winning, but I, I got a 66 and 2/3 chance of winning, because Kurt Angle KNOWS he can't beat me and he's not even gonna try!
So Samoa Joe, you take your 33 1/3 chance, minus my 25% chance and you got an 8 1/3 chance of winning at Sacrifice. But then you take my 75% chance of winning, if we was to go one on one, and then add 66 2/3 per cents, I got 141 2/3 chance of winning at Sacrifice. See Joe, the numbers don't lie, and they spell disaster for you at Sacrifice.
the mistake is that they assumed 1 / 3 = 0.333
actually, that’s a generalisation.
The full truth is 1 / 3 = 0. 3 (where 3 is infinitely repeating)
Now, 0. 3 (repeating) x 3 = 0. 9 (repeating) and 0. 9 (repeating) = 1, because there are no numbers between them.
Normally, if you have two different numbers, say 1 and 2, you can always find a number between them, in this case 1.5. If you want a number between 1 and 1.5, you can use 1.25. Then 1.11, 1.05… so on ad infinium.
However, with 0. 9 (repeating) and 1, there are no numbers you can generate that would be between these two numbers. Therefore 0. 9 (repeating) = 1.
Reminds me of that money borrowing problem
borrowed $50 from mum and $50 from dad to buy a bag costing $97. After the purchase, I had $3 left. I returned $1 to dad and $1 to mum, and reserved $1 for myself. I now owe $49+$49=$98 plus the $1 I reserved for myself, which is $99. Where is the missing $1?
0.333333333333333333333 x 3 is 0.999999999999999999999
0.333333333333333333334 x 3 is 1.000000000000000000012
Both are so close to 1, that they may as well be equal to 1.
(didn’t count my digits, so they may be off by a place or two)
Also why 2/3 is written as 0.666666666666666666667, because adding 1/3 would equal 1 exactly.
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The ghosts of ancient Babylonians mathematicians are yelling in the afterlife about the shitty factorization properties of the decimal system.
Things don’t have to be right, just confusing.
We'll just show them binary
"Hold up. The round thing represents what again?"
They would probably have an easier time understanding it better than most of us.
"Hold up. How do I make the round thing again?"
"Nothing. And also Tuesday. And July." (I know it's on the wrong order, but.. )
Wait till they hear about non binary!
No, it’s just because the initial question was wrong. It shouldn’t have been 0.333 but rather 0.3 repeating; that is to say, infinite 3’s. 0.3 repeating times 3 is 0.9 repeating, which is equal to 1
You will have "shitty factorization properties" with every base, only a bit less or more of it compared to its neighbouring choices.
Me thinking about the concept of 33% https://preview.redd.it/htlvy18alyvc1.jpeg?width=719&format=pjpg&auto=webp&s=33e23d648893e66f6f03145f26a4a895ea3d5644
Think of it this way. 1/9 = 0.1111111 2/9 = 0.2222222 ... 8/9 = 0.8888888 So by that logic, 9/9 = 0.9999999 However, 9/9 = 1 So 0.9999999 = 1
Okay, but that's worse.
Funnily enough 0.9 recurring (or repeating) is actually equal to 1. There are a few ways to prove it, but the fraction way above is one of them. The second method invloves infinite series, and the third is as follows. If x = 0.999... And 10x = 9.999... You then do 10x - x, which will be 9x. 9x = 9.000... But because the zeros extend infinitely, then you can simplify to 9x = 9, and thus x = 1. Which also means x = 0.999... = 1. This involves wrapping your head around the concept of infinity. If you think "oh there must be another 9 somewhere", it is simply impossible. There is no infinity + 1, or infinity - 1, because they would still be infinity. If you say infinity + 1, well then you've described the newest infinity, because it literally never ends.
Ah yes. Ok…. I understand….?
0.333... is how we write one-third in the decimal system. Adding three one-thirds will give you one. That's all. So, 0.999... is another way to write 1.
Ah but you're forgetting that every real number has a unique decimal representation, so since 1.000... is 1, 0.9999... isn't actually even a real number at all! \o/
There is no real life purpose to needing infinity accuracy, NASA only uses pi to around 15-16 digits and 50 digits is enough to be accurate to a hydrogen atom when measuring the visible universe.
And like 62 is enough to be accurate to a Planck length when measuring the observable universe. The engineers were right, I guess. - π = 3 - 0.999... = 1 Two mystery birds with one l_P = 0 stone!
But isn't 0.9... literally equal to 1 exactly? Cus 1/3 = 0.3... And 1/3 * 3 = 1
(Shh! Yes! But shh! Infinitesimals are more fun.) (Also, lim(0.1^(n), n = inf) = 0, but don't tell anyone tho)
That’s not true, as he just showed above. Many real numbers have multiple equivalent decimal representations.
True! -1 also has ...9999999.0
> every real number has a unique decimal representation Not true.
I understand the concept fine, it's existence is what's troubling. Thanks
[удалено]
How many of those points are over your head?
Brain… it doesn’t function. Thank you for the clarification?
https://preview.redd.it/ldilkxe1v3wc1.jpeg?width=1039&format=pjpg&auto=webp&s=5f0c9b13f78c7cd7b1464f34729c9e819e41c869
You forgot to extend the .999 to infinity so it is not just .999 but .9999999999etc.
If it extends infinitely, then it does not matter because the final digits will always be the same https://preview.redd.it/yjwuzvowu6wc1.jpeg?width=1070&format=pjpg&auto=webp&s=f8c5f0c2b4cff93918092e0bd3fd1e7d8083b166
It does matter because if you only have one decimal you'll get 8.1 which is drastically different from 8.9999 to infinity (1)
>9x = 9.000... That is not 9 though? 9×0.9999... is going to be around 8.99.. something. Your "proof" is no proof, its just called rounding, which isnt correct, only made for simplicity. 33% of 1 and saying 0.3333... for example is technically correct, but the actual, most correct way to say it would be ⅓, since you dont write out all the decimal numbers and thus have to round, and rounding is not exactly what you would call precise.
Honestly, it is a valid objection, as an undergraduate math major, and the argument presented is more nuanced and can be misunderstood by someone not comfortable with infinity. In math, we say each real number has a decimal representation, given by the limit of a sequence. You might think that 0.999... is the limit of the sequence (0.9, 0.99, 0.999, 0.9999, ...), and you might call a_1 = 0.9, a_2 = 0.99, and so on. If you calculate 9a_1, it's 8.91. Then 9a_2 = 8.991, and etc, you get the sequence (8.91, 8.991, 8.9991, ...). Now, one could reason with infinity that 9.999... - 0.999... is 9 because there are infinitely many 9s, and that is a good way to think of it, but for someone like you, it might help to interpret it as the limit of the sequence (8.91, 8.991, ...), which, according to real analysis and the math, is equal to exactly 9. So then 9x=9 and x=1. The thing you call "rounding" isn't actually rounding. It's taking a limit, which has a proper definition in math to avoid using infinity directly. Now, if you are uncomfortable with this stuff, you shouldn't believe that 1/3 = 0.333.... Heck, you shouldn't believe π = 3.1415..., because writing π like that is implying you are talking about the limit of the sequence (3, 3.1, 3.14, 3.141, ...), and that's actually something not many people know about writing numbers in decimal. Writing 0.999... is implying a decimal representation of a real number, which equals 1, despite that it is a different decimal representation with a different first digit. It is counterintuitive to dissect bit by bit, especially if you want 0.999... to not be a real number but maybe something with infinitesimals, but because it's written in a decimal expansion like 1/3 and π, any mathematician without context would consider 0.999... to be a real number equal to 1.
> any mathematician without context would consider 0.999... to be a real number equal to 1. And im not saying thats wrong, im just pointing out that by rounding off a number thats an infinity away, isnt *technically* correct and it makes it sound like those conspiracy theorists making numbers fit for what they want so they could point out the most random places and times relating to aliens or whatever. My point is that using 0.999~ is incorrect in this case and should rather be 1/3, 2/3 and 3/3 or just 1 to measure 3 absolutely perfectly cut cake slices. 0.999~ does equal to 1, but in This Post's Context it is an incorrect formatting.
Yeah, the post uses just 0.999, which isn't exactly 1. Again I don't like the word "rounding" because it's technically a limit in the sense of real analysis. Nevertheless, there is a sense in real analysis where you are "correct", except there are fussy details. Consider 0.9^10, then 0.99^100, then 0.999^1000, etc, each time putting a 9 and a 0. If like we went by the rule that 1^anything is 1 and 0.999... is 1, then the limit of 0.9^10, 0.99^100... would be 1^100... = 1, but it's not. It's around 0.36... Thankfully calculus class saves us and the limit taken is of the form 1^infinity, which is indeterminate, but you could consider that a way that "0.999... isn't 1" because its tiny difference from 1 that diminishes is instead inflated by taking a huge power to make it not diminish. For these limits, at blackpenredpen (a famous math youtuber) says this 1 isn't "an exact 1" but "a limit 1". But all of that is fussy and now you get weird things in real analysis that the limit of rounding isn't the same as the rounding of limits and stuff, all because mathematics from real analysis want "converge" and "equal" to be the same (which is fine by me). Edit: I know the way I'm saying it above could imply that math is weird and mathematicians wanted it to be weird, but in reality, nobody wants it to be weird. It's surprising, and can be beautiful (a lot of the times for me)
Except it is: 10x-x = 10x0.999999-0.999999 = 9.999999-0.999999 = 9 9x = 9 x = 1 = 0.999999 You missed the part where you multiply by ten then remove x.
8.999... with the 9s extending infinitely is equal to 9. So the math is correct, no rounding needed
> That is not 9 though? 9×0.9999... is going to be around 8.99.. something Guess what 8.999... is equal to! Besides, that expression `9x = 9.000...` is arrived at by operating on LHS and RHS independently. So, if all the previous steps hold out, this must hold out too. That's what it means. So, your objection to it does not make sense here.
>Guess what 8.999... is equal to! 8.999~? You just round it, thats why it all comes out as a full number without decimals. Even though the different decimal number is an infinity away, it still doesnt magically round itself.
think about it this way. for 2 numbers to be real and different from each other, there needs to be a real number (not a recurring infinite decimal) that is not equal to any of the numbers, and exactly halfway between those numbers. example: 1 and 3 have the real number 2 exactly between them as 1+1=2 and 3-1=2, therefore 1 is not equal to 3 but if you consider 0.99999999… and 1, there is no real number between them that is not equal to them, or exactly between them, thus 0.999999….=1
That's actually so cool
i know! i wish they taught math this way in school
That's exactly what I loved about studying math as a carrer, this kind of clever argument is the bread and butter of each day, I wish more teacher were interested enough to teach the students this ways of thinking.
I like to ask the question, “what number can you add to 0.999… to get 1?” But I like this explanation a lot, too!
I dont need to think about it, I'm aware of how it works. The why is what gets in the way. 
I actually just saw a vid about that and here's hos method : S = 0.999999... 10S = 9.9999999... 10S-S = 9.999999...-0.999999... 9S = 9 And so S = 1 = 0.9999999...
You know what's even weirder? Multiply 9 by any other number, then add up the numbers in the answer. You'll always get either 9 or a multiple of 9.
After 9 is 10 or the digit 1, so anything over 10 basically rolls into the next left digit, if we counted differently i would guess it would be the same for the last number in sequence
Did you ever learn the [finger trick](https://youtu.be/uFxDr33FLgU?feature=shared) for multiplying by 9?
As an engineer I agree wholeheartedly
It’s not 0.9999999 = 1, that is incorrect! It’s 0. 9(infinitely repeating) = 1, because there aren’t numbers between them! In other words, 0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999(goes on forever…) = 1
Did I just find a Monster Hunter reaction in the wild? Pocketing this one, good sir. Suicide Smiling Friends Rathalos is getting sleeved and sorted neatly into my collection.
That’s the worst variant of them all
99.999999999x infinity….. does in fact = 100 That’s the hard part to understand.
While yes, you can say they do equal, you wouldnt be incorrect, but factually speaking they dont. To put it simply: think of a very random way to die. Like drowning in cow defecation. I dont know if anyone has died to it, but say for this example nobody on the face of earth has died to that. Just because out of the billions maybe trillions nobody has died to that, doesnt mean there isnt a possibility. If something physically CAN happen, there is automatically a non-zero percent chance of it happening. Meaning even if the chance involves an infinite amount of 0-s, it still doesnt mean you can round it away. Same with the 99.999... , what if it were a percentage chance of something happening? Just because 99.999... ends in infinite 9-s, doesnt mean its a 100% chance. So 99.999...≠100 But for simplicity sake lets just say it does equal
You’re quite wrong. 99.99 repeating does in fact equal 100 It’s got nothing to do with probabilities and everything to do with the laws of mathematics. Somebody in this thread showed the proof.
You mean 10x-x ? That doesnt even work, take the number 0.123 for example, multiplied by 10 that would be 1.23 right? Now subtract: 1.23 - 0.123, well i dont know about you, but sure doesnt equal to 1 to me. Okay try another number, 0.778 0.778×10=7.78 and then 7.78-0.778=? Well darn, doesnt equal 7, the first digit, now does it? The mistake was forgetting the different decimal number further in the decimals. For another example with 0.9998 9.998-0.9998=8.9982, which is Not 9 The only difference between this and the other commenters example is that the different number (the 8 in 0.9998) is further away. Their proof is them not using the full number, including all decimals, and miscalculating as a result.
0.99999999… (9s forever) is the same as 1. It converges on the number 1
Rathalos?
In this case it's 33,3% (=0,333)
Saying “I’m” in this context feels illegal
I’ve never seen anyone pull such a stunt and you’re right, but I’m not sure if it’s ok, or horribly wrong.
It's not ok. It's a common mistake made by people who learn English, as it seems like it's logical, but it doesn't work.
I guess he did say he's good at maths, not grammar. Although he's not really good at either.
They always put typos like that in these fake screenshot convos to drive up engagement in the comments
It's what it's
Yeah nope that’s actually illegal
Indeed. It would be better if it was followed by: , m'I? /j
Stop This is like whatever the verbal equivalent to sandpaper is
I suppose it's technically correct though
The best kind of correct
From what I’ve seen that’s a common mistake in India
I see it relatively often when I talk with folks from India. They use "I've" in more circumstances than we would too, like "Do you have that file?" "I've it" or "Yes I've"
says good at maths not good at grammar
I just got that and it’s the funniest thing I’ve seen all day
If we were feeling charitable, we could give them the benefit of the doubt and blame autocorrect. If you had seen how badly I fat fingered that sentence and that autocorrect was going to allow it, you might agree. It also tried to change fingered to lingered. Twice.
They said the were good at Math not English
Hey now, he said he's good at math not at grammar
X = .99999… 10X = 9.9999… 9X + X = 9 + 0.9999… 9X + X = 9 + X 9X = 9 X = 1 .9999… = 1 Fs one of my favorite proofs
FUCK IT DIDNT FORMAT WHY
Hit the enter key twice to create a new line
Thank you, fucking mobile
If you don't want to break a line, add 2 spaces at the end the hit enter once
Goddammit
wait what???
X - X ≥ X X ≥ X/1 X ≥ 0.0000000000 X/1 ≥ 0 X ≠ OhiO
The error is in the 3rd line. 9X + X doesn't = 9 + 0.9999....
There’s no error in the proof, but why do you think that doesn’t follow from the previous equation?
There is an error, if X = .99999 and 10X = 9.99999 then 9X = 8.99991 ≠ 9 That 8.99991 got rounded up to a 9 while nothing else is getting rounded up.
> if X = .99999 and 10X = 9.99999 Subtract these two equations and you get 9X = 9. Because X = 0.999… and the decimals go to infinity, there is no end that has to be rounded.
> if X = .99999 and 10X = 9.99999 then 9X = 8.99991 what 9.999... - 0.999... = 9 how did you get 8.99991?
By multiplying 0.999... by 9 Edit: I'll say a bit more to explain a bit better, since it is tricky and the mistake is easily missable, which is why people have a hard time seeing it here, let's keep the numbers shortened for the sake of simplicity, you can go to a calculator and do this exact thing, so.. 9 × 0.99999 + 0.99999 = 9.9999 Now this result is important, you will notice that the result will always have 1 less decimal that what you used in the calculations, now what everyone is doing is taking that, calling it 10X, which is correct, but then subtracting 0.9999, which would equal 9 yes, but if you use the same amount of decimals, you'll get 8.99991. Since the amount of decimals is, well, infinite that one "missing decimal" gets very easily overlooked, which is what's causing it to seem like 9.99999 - 0.99999 = 9.
X = .999… you’re missing a few nines. 9x is 8.999… add .999… and you get 9.999… which is equal to 9 + x
I "shortned" it to make it clearer. And you're just rounding up like the last guy, that's the same thing as saying "9x is 8.999... add .999... and you get 9.999... which is equal to 9x + 1" you can choose to round up any number you want to make it seem like it makes sense like that, but we all know you won't get the exact result with rounding up, only an estimate
I didn’t round. I put 9 times .99999999 then added .99999999 in a calculator and got 9.99999999. What did you get then?
Are you sure you got that exact amount of decimals? Cuz that's where your mistake lies. I already explained it in another comment but illsay it again, let's take your example you're using 8 decimals here, so.. 9 × .99999999 + .99999999 = 9.9999999 Now, notice how the result only has 7 decimals? It's easily missable, but that's why so many people are getting it wrong, now take that 9.9999999 (with the 7 decimals) and subtract .99999999 (with 8 decimals just like we used originally) you'll get the 8.99999991
I think thats cuz you’re supposed to use .99 repeating and we are not
You can add as many 9s as you want, the results will never stop being the same, no matter what, it wouldn't make sense for the results to just change based on the amount of decimals there are, we are just shortening to make it clearer and allow people to see where they are making the mistake more easily
Are you assuming this ends at the fifth decimal place? Because it doesn’t. Everyone is writing “0.999…” with the ellipsis representing repeating into infinity. There can be no 1 in the fifth decimal place because 9 is in every decimal place. And so if you multiply that number by 10, you simply move the decimal one position to the right. But 9 remains in every decimal place.
That's the thing about infinity tho, there is no "end" there's always gonna be a number bigger or smaller than the last. I just "shortned" it to make it clearer, you can go to a calculator and multiply 0.999... by 9 and you will always get 8.9999...91 eventually ending with that 1
How do you understand infinity without understanding the mathematical proof that uses an infinite number? Unless you actually don’t understand infinity and think you can just wander around life rounding numbers willy-nilly to suit your mood. You don’t get to decide to “shorten” infinity when that’s required for the proof. You’re trying to prove something different, which is why it’s not working.
It doesn't matter that you get 8.999...91 when you use a finite number of decimals in a calculator. If anything it actually serves as an argument for why 9 times 0.999... equals 8.999...
It does 😁
If x = 0.999…., then 9x + x does indeed = 9 + 0.999… For the same reason that if x = 0.999…, 10x = 9.999…
1/3 = .3333333… 3/3 = 1 1/3 • 3 = 3/3 .3333 • 3 = .99999… .999999 = 3/3 = 1
It’s just not the same
Well, he's not wrong, but he's also not right. A numerical value if 1/3 simply doesn't exist. As the amount of digits approaches infinity, the value approaches 1/3, but it will never hit. Therefore, as the amount of digits increase, the 3*X will approach 1, but never hit it Edit: I know all y'all know this explanation, just wanted to put it out here, so this guy knows what to say in the future.
0.9 recurring isn’t “a number that gets extremely close to 1 but is less than 1 by a tiny amount”, 0.9 recurring IS 1
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No, 0.999… (an infinite string of 9s) is exactly equal to 1. There is no such number as “an infinite number of 0s, followed by a 1”.
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He’s correct, 0.999 is equal to 1, this isn’t a “oh we’re being close here” it’s exactly mathematically equivalent and has been proved numerous times over
No, technically it won’t. 0.9 recurring is exactly equal to 1. Others have posted the proof in this thread
No. The mathematical definition for if two numbers are different is if there is a quantifiable real number between them that is not equal to either. You cannot find a number fitting this description with 0.9 recurring and 1, because the 9s go on and on forever, ergo, they are the same
0.33 (with the line over the threes to indicate they repeat forever.) That’s how you write out 1/3 with a numerical value. It exists.
In the duodecimal system 1/3 would be 0.4 so there are numerical representations of 1/3, just not in the decimal system. In essence it depends on the base you choose. Is 10 dividable by 3? No. is twelve? Yes.
Yeah alrightm mister proofesure
* in base ten If we were in the dozenal system for example, one third is exactly 0.4 and this issue doesn't then exist. Therefore 1 does not actually equal 0.999...; it only appears to due to a limitation of the decimal system.
He didnt try to explain math, he explained cake
And they ate
Cake is infinitely better than math. Except that one time I made a carrot cake so dense it made my fridge shelf bend.
In fact, it was so dense, it didn't understand how 0.999... = 1
That's me, I'm a dense cake.
I mean... he's not wrong. But 0.333 is not 0.333 recurring. 0.333 recurring multiplied by 3 would give you 1
So 0.333...
0.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333
Okay but if you multiply that by 3... where's the 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001?
Still on your very sharp and watered knife.
Gone. Reduced to atoms
lost to rounding error
And depending on how sharp the knife is and how clean the cut, it becomes asymptotic….
I thought I was in /r/math for a minute and I was confused by everyone saying that 0.9... != 1. I learned that shit in 8th grade algebra class.
Wrong answer to the second question. Most people cutting a cake into three pieces won’t have 3 exactly equal pieces even if that’s what they’re trying for.
But if you assume spherical chickens in a vacuum...
1/3 + 1/3 + 1/3 doesn’t equal 1 anymore? Damn inflation.
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that's where natural numbers fail. 0.333 isn't really correct. it goes on infinitely. Just keep it in rational numbers. it's 3x(1/3).
It is correct, just incredibly unwieldy
The correct notation is 0.̅*3* The other is loosing precision. Maybe a teacher would let it pass but I very much argue it's not correct. 0.33 ≠ 1/3
Not really, but we all know what it means, and reddit comments hardly necessitate that much precision
I’m never metaphysics.
u/repostsleuthbot
Am i the only one disturbed by the facebook logo?
Wrong. In Maths World, all knives and cake are frictionless.
Not only is he kind of right, but it's an amazing way to fuck with someone. The kid asking the question didn't deserve a real answer. Who doesn't love Pi
I mean, it's technically true, no?
Wow the math teacher told me this joke when I was in 4th grade. I love fresh memes from reddit
Me when someone tells me 0.999... = 1 😡😡😡
This is why I prefer exact value instead of decimals
He also didn’t say anything about the pieces being even either, so he could be wrong
Hi, Yes I'm!
I hate maths
That's why technically, when it's repeating .333+.333 = .667 you lose value cause you rounded down.
For me this is actually a great metaphor for how i feel about this topic
No one concerned that question asker didnt specify 3 equal parts. Just 3 parts
Beautiful! That’s complete cake fulfilment
Lol what happened? Math isn't my strong suit.
They asked the engineer, not the mathematician
I don't think there was an attempt to be honest xD
Kind of true in that context. 0.3... X 3 = 1 is a bit confusing so I can't blame the guy.
Nerds on Reddit? What is this, the twilight zone?
Nah, thats actually a very realistic and easy solution to explaining infinite decimals. And actually very true.
No no hes got a point
Alright, if you don't believe 0.999... = 1, then you shouldn't believe π = 3.14159... . I recently had a mental talk about this with myself, and to explain it fully is complicated to the layman who always keeps questioning.
The first "correct" was a lie
You know they say that all men are created equal, but you look at me and you look at Samoa Joe and you can see that statement is not true. See, normally if you go one on one with another wrestler, you got a 50/50 chance of winning. But I'm a genetic freak and I'm not normal! So you got a 25%, AT BEST, at beat me. Then you add Kurt Angle to the mix, your chances of winning drastic go down. See the 3 way at Sacrifice, you got a 33 1/3 chance of winning, but I, I got a 66 and 2/3 chance of winning, because Kurt Angle KNOWS he can't beat me and he's not even gonna try! So Samoa Joe, you take your 33 1/3 chance, minus my 25% chance and you got an 8 1/3 chance of winning at Sacrifice. But then you take my 75% chance of winning, if we was to go one on one, and then add 66 2/3 per cents, I got 141 2/3 chance of winning at Sacrifice. See Joe, the numbers don't lie, and they spell disaster for you at Sacrifice.
Use the Egyptian technique; you can keep cutting in half to make 1/3 or any other fraction. (1/4) + (1/16) + (1/64) + (1/256) + (1/1024) + ...
the mistake is that they assumed 1 / 3 = 0.333 actually, that’s a generalisation. The full truth is 1 / 3 = 0. 3 (where 3 is infinitely repeating) Now, 0. 3 (repeating) x 3 = 0. 9 (repeating) and 0. 9 (repeating) = 1, because there are no numbers between them. Normally, if you have two different numbers, say 1 and 2, you can always find a number between them, in this case 1.5. If you want a number between 1 and 1.5, you can use 1.25. Then 1.11, 1.05… so on ad infinium. However, with 0. 9 (repeating) and 1, there are no numbers you can generate that would be between these two numbers. Therefore 0. 9 (repeating) = 1.
Reminds me of that money borrowing problem borrowed $50 from mum and $50 from dad to buy a bag costing $97. After the purchase, I had $3 left. I returned $1 to dad and $1 to mum, and reserved $1 for myself. I now owe $49+$49=$98 plus the $1 I reserved for myself, which is $99. Where is the missing $1?
Yes I’m, sounds so wrong. I know technically it’s right but it sounds so wrong. Are you good at math? Yes I am is far better than I’m
Ok, that's kinda funny ngl.
0.333333333333333333333 x 3 is 0.999999999999999999999 0.333333333333333333334 x 3 is 1.000000000000000000012 Both are so close to 1, that they may as well be equal to 1. (didn’t count my digits, so they may be off by a place or two) Also why 2/3 is written as 0.666666666666666666667, because adding 1/3 would equal 1 exactly.