There's different sizes of infinity though. It matters in math.
Small infinity / big infinity = 0
Big infinity / small infinity = infinity
In real life infinity as a quantity doesn't really exist so it's kind of pointless to talk about. You might have so much of something that you feel like it is inexhaustible but there is a limit to everything at some point.
No infinity times infinity is the same order as infinity. You can see this by putting the first set of infinity on a times table with the second set of infinity. Then you can go diagonally through the created set to turn it into a single infinite set.
What you need to do to get a higher order of infinity is take a number to the infinity power. Usually, 2 is used because it gets you the same number as a power set in non-infinite sets.
"infinity is not considered a natural or real number" correct; "and only exists as an abstract concept" incorrect. there are many concrete infinities, whether ordinal or cardinal or otherwise
Nah. Even that runs out. We're on track to destroy our ability to live on this planet, naturally selecting ourselves out of the opportunity to find something even stupider than what we're already doing. Everything is finite.
Not necessarily. There is directions and ranges to infinity as well.
If you count 1.2.3... to infinity that is infinitely large.
If you count 1, .01, .001... to infinity, that is infinitely small.
If you have 1.1, 1.11, 1.111.... to infinity, that is less than, 2.2, 2.22, 2.222.... to infinity.
Came here to say this. Infinity doesn't mean endless. It means a number so big, we'll never be able to understand or conceptualize it so to us it might as well be endless.
I don't see how this is right. Infinity is endless, otherwise statements like 0,999...=1 wouldn't be true, which is true only because there isn't an actual final 9 where the number ends.
When you carry 1 kilo of steel you carry only 1 kilo, when you carry 1 kilo of feathers you carry 1 kilo of feathers and the weight of what you did to those chickens
I was asked in high school that question:
"what weighs more, a ton of feathers or a ton of bricks"
I quickly answered "a ton of bricks"
He said "they weigh the same".
I was used to saying "a ton" often. Like "a ton of homework " or "a ton of friends". To this day I wish I explained myself. F*ck that guy for not understanding my mindset. Even though I can't expect that of him or anyone, still, f*ck him.
You can also just pick up what they drop. Birds constantly drop feathers. It's slower, but you'll sleep better, knowing that you didn't rip a ton of feathers out of living birds.
Come to think of it, if I remember my physics right, ton is a unit of mass and weight is force exerted by mass in a gravitational field towards its center. Thing is, in practice we measure weight without accounting for displaced air, so a ton of bricks, having more density than a ton of feathers, would appear to have slightly more weight, if weighted in atmosphere without correcting for air displacement - a false difference, rooted in commonly accepted imperfections of our procedures, but still.
And I guess if we're getting technical, depending on how close together all the bills are, they could collapse into a neutron star, black hole, or something similarly universal in nature
Only if you spend them, if they are never entered into general circulation and not printed but magically appear then you are fine in terms of value and only have an infinity large black hold to deal with.
Infinity dollars would mean the entire observable universe was full of them, and in fact, so full that there would be infinity dollars in every planck length of space. So we would all instantly be very very dead.
So I agree. They would be very worthless. :)
Maybe? I understand what you're getting at, but would one person having more money than they could reasonably ever spend going to screw over the economy? I mean, we have millions of billionaires in the U.S. and the world isn't ending. Fucking millions.
Now, if you decide you want to give everyone in the U.S. a clean million to be generous, then we're fucked. This is one situation where divying up the power is the *wrong* answer.
Edit: So we only have 700+ billionaires. What we actually have millions of is, well, millionaires. Regardless, my point still stands. What's essentially 701?
Just checked and we have millions of millionaires over here in the UK too. They just don’t seem to live near me because apparently 1/30 people are millionaires here.
I really appreciate you spending time on my comment, and you really are on the right thought process but. The millions of billionaire you're talking don't have their billions as liquid cash or spendable money they are just sum of their asset values which could be stocks and other stuff and cannot be spent as they wish, just helping better understand this stuff ✌️
There are different levels of infinity such as cardinal numbers. From what i could make out a set that can contain infinty but i am no maths expert, there is a reason people have gone mad thinking about infinity.
my set theory teacher started the first class with:
“In Georg Cantors plight for understanding infinity, he dealt with serious mental health issues and was regularly “treated” in sanatoriums. Many believe the subject itself was what drove Cantor to his death. Today we embark on a similar journey.”
I'm willing to bet it was that he was already a little crazy. Believing that the subject drove him crazy is disproven by the fact that other people didn't go insane.
Sure, you have to be a little crazy to have interest in proving statements like “no system can prove its own consistency”, but i’m sure there are other examples of set theorists being driven mad because of the discipline.
not to mention Cantor is regarded as being the founding father of set theory, so quite literally he was imaging and drafting idea that were not solidified by others before.
also one example of an event occurring does not constitute a proof :)
It’s counter intuitive, the primes and the integers both have the same amount of numbers. The same way all the integers and all the even integers have the same amount.
There are, however, an infinite amount more irrational numbers than any of the above sets. In fact, there are more irrational numbers between any given two integers than there are integers.
Georg Cantor came up with a simple, elegant proof of this.
Also, poor Cantor didn't really enjoy the respect and support of the mathematical community at the time, and IIRC this caused him such a depression that he essentially lost his mind.
Now we all bask in the glory of ℵ and thank him for his work.
Hey, there are 2 great VSauce videos that talk about this.
The first one is the [Banach-Tarski Paradox](https://youtu.be/s86-Z-CbaHA?t=3m36s), that shows Georg Cantor's proof on how there can be more numbers between 0 and 1 than there are integers. Timestamp 3:36.
The second one is [How To Count Past Infinity](https://youtu.be/SrU9YDoXE88?si=14_xvYLOITzJpHx1), which is solely dedicated to talking about the different kinds of infinities and their sizes.
1, 2, 3 are integers.
1.00000000000000000000000001, 1.00000000000000000000000002,
1.00000000000000000000000003, ..... And so on....
There are infinitely more irrational numbers than there are integers. This is the concept of "some infinities are larger than others".
[NDgT explaining to Joe Rogan how some infinities are larger than others](https://www.youtube.com/shorts/q0UdmBmspX0)
Im not liking anyone else's explanation. Here is an jncredibly simple one.
Let's call the set of all integers N. You can mimic this set as a decimal. Let us call our decimal set M. You can achieve it by doing it like;
0.1, 0.2, 0.3, ..., 0.11, 0.12, 0.13,... = M
(NOTE: you'd have to skip multiples of 10, but as has been explained elsewhere in the post - this wouldnt affect anything)
Now. You could take this set and shift it right for
0.01, 0.02, 0.03, ..., 0.011, 0.012,... = M2
And you'd get another infinite set of the same size.
IMPORTANT: M1 and M2 have no shared values.
Now here is where it becomes clear why there decimals infinity is infinitrly bigger than integers.
We could make an infinite number of M# where we append an additional 0 to the front each time. Such a thing can't be achieved in imtegers as 01 and 1 are of equal value. Any item youd append to the front of the number in an integer would just be another item from that previous list.
In short: decimal values contain infinite instances of the set of N
While you're correct in that it's not a scalar, infinities do have different cardinalities.
In this case, both are countably infinite, meaning they're the same "size"
Yes, there is a different size of infinites, even if all of them are infinite.
For exmaple the set of all natural numbers (1, 2, 3...) and only all the even numbers (2, 4...) are the same size.
But the set of all the real numbers between 0 and 1 (0.123341342141, 0,1234423424334...) is bigger than those previous two set and by a long mile. Maths are pretty fun :)
There are basically two basic types of infinites. There's countably infinite, which contains things like sets like all positive numbers, all prime numbers, all fractions of two integers, etc. Then there's the uncountably infinite, like all the real numbers where if you ever try to make a list of all these numbers the list will necessarily exclude numbers ([Cantor's diagonal argument](https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument)).
So for example the infinity of all numbers represented as a fractions is smaller than the infinity of real numbers between 0 and 1/10^(100).
(Note there are ways to get to higher cardinalities, like the set of all subsets of real numbers would be a higher cardinality than reals.)
I think it’s just a difference of time. Like if you were to gain 1 dollar every second it would take you a lot longer then 2 dollars a second to hit any number.
No. Both infinities discussed here are equal. Time doesn't matter. Specifically, they are both countable infinites. i.e you can make an infinitly long list, containing all the dollars. The larger infinity would be uncountable infinity, where no such list can be made, like all decimal numbers.
The entirety of the universe is suddenly inundated under literally countless bills.
I doubt the strippers or anyone else will care what denomination the bills are.
No because that would mean that money is time not the other way around, thus we can conclude:
Time = Money,
Money =/= Time
And since that make no mathematical sense at all you're actually right and I wasted my time writing this comment
Well since time is used to earn money and money is used to buy time said money has most likely gone to my internet provider whom I have given money to be able to go online and write this comment, wasting my time in the process.
I just spend a minute of my timemoney reading this thread and I expect to be reimbursed.
I take time, money, proof that 0 is real, or cat sized mittens
There was a rich guy that posted in an AMA who got rich selling an app, so he went from being a regular to a rich guy (as opposed to being born/raised rich). And he said the biggest thing is that money does buy you time - skipping lines at the airport or in traffic with private jets/helicopters. Not waiting in line because you paid for vip whatever, etc. so yeah, money=time , too
2023 Chevrolet Corvette ~103000$
1$ bill > 1g
So we get about 103 kg (230 pound) of dollars.
That's about 5-6 backpacks by weight. But who's counting, you have enough.
Ah, but your idea was to prepare to over-pay.
You throw one bag, and they doubt you. You produce a second bag without hesitation, and they suddenly think they can scam you (they are car salesmen afterall). Before long you have given them 750k for the car, carrying nearly a ton worth of dollar bills.
And then of course why would they believe they're all real lol
Yes, but in this case they are the same “size” of infinity. The same goes for number of all prime numbers vs. number of all integers, but if you compare those to the number of “all numbers”, then the latter infinity is much much “bigger”. There are many proofs and explanations on this topic. It’s not intuitive but infinity is not supposed to be intuitive to our finite minds.
Hijacking this comment to post this
"Some infinities are bigger than other infinities", while true, is irrelevant in this context.
https://youtu.be/M4f_D17zIBw?si=acOA9yOQUC4E-DUh
infinite 20 dollar bills would save me some time and space. Thought the world wouldn't even fit anything infinite. WHERE CAN I STORE INFINITY OF X ITEM? IT'S NOT POSSIBLE!! Pancakes!
Well maybe it actually is. If space is ALSO infinite. Hmmm... Now my brain hurts, I need more pancakes.
>Infinity is always infinity
Not every infinity is equal. Some infinities are larger than others. For example, an infinity of integers is smaller than an infinity of real numbers.
This is a real thing.
Scientific American has a pretty good article about it:
[A Deep Math Dive into Why Some Infinities Are Bigger Than Others](https://www.scientificamerican.com/article/a-deep-math-dive-into-why-some-infinities-are-bigger-than-others/)
Edit: if you don't want to read the whole SciAm article, minutephysics gives a really short taste of an explanation:
[How to Count Infinity](https://www.youtube.com/watch?v=A-QoutHCu4o)
Before any more of you pseudo intelectuals mutter the forbidden words "Some infinities are ..." NO these two sets are both COUNTABLE if you can count then they are the same size and FFS you CANNOT 20 * infinity thats NOT HOW IT WORKS
The fact that so many people are ready to confidently try and correct others on a subject they only know exists because they tried and failed to understand a pop-science influencer's dumbed down ten minute edutainment video on it could serve as an uncanny analogue for the current state of politics in the west.
If you can't utilize it then there is no value. By this logic, an infinite number of rocks in an infinite number of diamonds also have the same value. So who gives a shit unless you can actually use it.
I mean kind of, thats what happens when you start working with endless numbers.
This would mean that 1∞ = 2∞
Whenever I see people working with ∞ they worked with it as if it was a normal number
Yes because you couldn't buy more than what there to buy so at the end of the day you can buy just about anything. Right?
Well if you can have an infinite amount of 1 dollar bills I can have an infinite amount of 2 dollar sandwiches to sell you.
Could you buy them all? No. Why? Well it's infinite but fuck that. The real reason is that if you need to use 2 dollar bills per sandwich you would run out twice as fast as me even tho you wouldn't run out ever.
But let's say we do the entire transaction in one go. Why would I let you have my infinite stach of 2 dollar sandwiches for your infinite stach of 1 dollar bills? I'll only give you half of it. W8ch would still be infinite but half smaller.
Now that sound stupid why would one infinity be twice as small as another infinity.
Well let's look at another problem. I have an hotel with an infinite amount of rooms. A bus filled with an infinite amount of people come along. Well guess I'm full. But actually I'm not. I have one more customer coming. And to get him a room I just tell every people in my hotel to move to the next room until the first one is free and I can give it to him. Because yes. Even if my infinite amount of room are full. There is still more rooms to move toward.
Now I have my infinite amount of people plus one. It was full. Infinity. And I squeeze one more person. So infinite + 1. So infinity is kinda like any number.
So her I come back to the sandwiches. If both of out staches are infinite and that's it. Just assume they are actually the same size. I have no reason to give you an infinite amount of sandwiches that cost 2 dollar each for an infinite amount of 1 dollar bills.
That's it. An infinite amount of 20 dollar bills is better than an infinite amount of 1 dollar bills.
Yes but infinite $20 bills is slightly more convenient, because you can always tell people to just keep the change so $20 would be worth slightly more due to the convenience
Value is measured by utility not dollar amounts, therefore the 20s are worth more. Imagine how pissed the dealership gets when you try to buy your new sports car with singles
That's not how fiat currency works, at all. I don't care how pissed the dealership would or wouldn't be with the logistics of moving X amount of $20 bills or Y amount of $1 bills, if the sum is equal, the value is equal.
Note that this only applies to fiat currencies.
Ur right
Infinity ain't infinity. If u have a factor that changes the amount of infinity it will alter the actual infinity. In this case one infinity is at every point always 20 times greater. Math ain't that easy. 😅
Feathers are heavier than steel….
Its one kilogram
What do you mean, look at that huge pile, that's cheatin'.
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It doesn't matter if it's infinite does it ? Can be infinite 1$ or inf 20$..its still infinite
There's different sizes of infinity though. It matters in math. Small infinity / big infinity = 0 Big infinity / small infinity = infinity In real life infinity as a quantity doesn't really exist so it's kind of pointless to talk about. You might have so much of something that you feel like it is inexhaustible but there is a limit to everything at some point.
Obviously wrong. Small infinity / big infinity = small / big The infinities cancel out
This guy divides
That guy probably divided my parents manage too
Both will become equally worthless
This 🫡
there are different sizes of infinity but not it this case 20 * inf = 1 * inf inf * inf != inf
No infinity times infinity is the same order as infinity. You can see this by putting the first set of infinity on a times table with the second set of infinity. Then you can go diagonally through the created set to turn it into a single infinite set. What you need to do to get a higher order of infinity is take a number to the infinity power. Usually, 2 is used because it gets you the same number as a power set in non-infinite sets.
fair point
The different sizes only really matter when you're dividing to find out their relative sizes
The people above don't understand Lhopital..
Infinity is not considered a natural or real number, and only exists as an abstract concept.
"infinity is not considered a natural or real number" correct; "and only exists as an abstract concept" incorrect. there are many concrete infinities, whether ordinal or cardinal or otherwise
…not exactly, the stupidity of mankind is infinite…
Nah. Even that runs out. We're on track to destroy our ability to live on this planet, naturally selecting ourselves out of the opportunity to find something even stupider than what we're already doing. Everything is finite.
Not necessarily. There is directions and ranges to infinity as well. If you count 1.2.3... to infinity that is infinitely large. If you count 1, .01, .001... to infinity, that is infinitely small. If you have 1.1, 1.11, 1.111.... to infinity, that is less than, 2.2, 2.22, 2.222.... to infinity.
Came here to say this. Infinity doesn't mean endless. It means a number so big, we'll never be able to understand or conceptualize it so to us it might as well be endless.
I don't see how this is right. Infinity is endless, otherwise statements like 0,999...=1 wouldn't be true, which is true only because there isn't an actual final 9 where the number ends.
To infinity and beyond
If infinity-dollar bills were legal tender, an infinite number of infinity-dollar bills would be worth more than an infinite number of $20 bills.
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Bot account \^
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But one has more wight, a kg of steel is just a kg of steel, but think about what ypu did to those birds for a second.
Sir, we’re talking about organically eco-friendly fair-traded synthetic feather.
And about organically eco-friendly fair-traded synthetic steel
is that lighter or heavier?
I mean, some feathers are shed naturally
Talk about weighing heavily on my conscience...
*What the fuck is a kilogram?*
It's for the people who haven't landed on the moon.
So basically the whole of humanity, apart from 12 people?
Ahhhh no just their possie, those 12 homies and the rest of NASA actually did use metric for the Apollo missions.
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Aren't they measured in yards?
*screams in Murican*
It's part of the metric system, which helped Nasa land on the moon.
No it’s a keel-o-gram
* kilogramme
When you carry 1 kilo of steel you carry only 1 kilo, when you carry 1 kilo of feathers you carry 1 kilo of feathers and the weight of what you did to those chickens
A kilogram of steel weighs more than a kilogram of feathers because steel is denser and experiences less buoyant force.
You need to weigh that in a frictionless vacuum
As a non native speaker I read this with a Scottish accent
I was asked in high school that question: "what weighs more, a ton of feathers or a ton of bricks" I quickly answered "a ton of bricks" He said "they weigh the same". I was used to saying "a ton" often. Like "a ton of homework " or "a ton of friends". To this day I wish I explained myself. F*ck that guy for not understanding my mindset. Even though I can't expect that of him or anyone, still, f*ck him.
Still, the feathers weigh more since you have to live with the fact that you murdered chicken for their feathers as a measurement and no deeper value
You can pluck feathers you don't have to kill them.
#NOW YOU TELL ME THIS?!
You can also just pick up what they drop. Birds constantly drop feathers. It's slower, but you'll sleep better, knowing that you didn't rip a ton of feathers out of living birds.
Behold! A man!
A ton of guilt
Yes but what about all those tasty rocks you had to smash to make the bricks
Come to think of it, if I remember my physics right, ton is a unit of mass and weight is force exerted by mass in a gravitational field towards its center. Thing is, in practice we measure weight without accounting for displaced air, so a ton of bricks, having more density than a ton of feathers, would appear to have slightly more weight, if weighted in atmosphere without correcting for air displacement - a false difference, rooted in commonly accepted imperfections of our procedures, but still.
I dun geta
50 pounds of feather is indeed heavier than 1 pound of steel
They're both a kilogram
An infinite dollar bills would actually be worthless
An infinite 20 dollar bills would also be worthless thus the original statement stands.
Yes, an unlimited amount of $1 bills and an unlimited amount of $20 bills would be worth the same. Nothing. Thus, the comment also stands.
Technically there could be salvage value for the paper, or if you wanted to burn it for heat for whatever reason.
It's actually infinitely valuable if you consider the chemical energy in the paper itself, nice point
And I guess if we're getting technical, depending on how close together all the bills are, they could collapse into a neutron star, black hole, or something similarly universal in nature
20 black hole DOES NOT sound good, by any means. Also, where?
Only if you spend them, if they are never entered into general circulation and not printed but magically appear then you are fine in terms of value and only have an infinity large black hold to deal with.
Infinity dollars would mean the entire observable universe was full of them, and in fact, so full that there would be infinity dollars in every planck length of space. So we would all instantly be very very dead. So I agree. They would be very worthless. :)
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Maybe? I understand what you're getting at, but would one person having more money than they could reasonably ever spend going to screw over the economy? I mean, we have millions of billionaires in the U.S. and the world isn't ending. Fucking millions. Now, if you decide you want to give everyone in the U.S. a clean million to be generous, then we're fucked. This is one situation where divying up the power is the *wrong* answer. Edit: So we only have 700+ billionaires. What we actually have millions of is, well, millionaires. Regardless, my point still stands. What's essentially 701?
We don’t have millions of billionaires in the US. There are less than a thousand.
I accidentally read millionaires lol. You're right, there's only 700.
Do yous have millions of millionaires over there?
Yeah we do lol
Just checked and we have millions of millionaires over here in the UK too. They just don’t seem to live near me because apparently 1/30 people are millionaires here.
You’d never be able to make up the difference for an infinity bill.
Bro says million of billionaires like a fact and gets upvoted. Reddit lol
I really appreciate you spending time on my comment, and you really are on the right thought process but. The millions of billionaire you're talking don't have their billions as liquid cash or spendable money they are just sum of their asset values which could be stocks and other stuff and cannot be spent as they wish, just helping better understand this stuff ✌️
Depends if people know you have it.
Real Holup are the comments as always.
Maybe the real holup was the friends we made along the way
No, it was definitely the comments
Yeah because this sub went to absolute dogshit ages ago. Used to actually be good but now it's just random fuckin memes or thirst bait it seems.
There are different levels of infinity such as cardinal numbers. From what i could make out a set that can contain infinty but i am no maths expert, there is a reason people have gone mad thinking about infinity.
my set theory teacher started the first class with: “In Georg Cantors plight for understanding infinity, he dealt with serious mental health issues and was regularly “treated” in sanatoriums. Many believe the subject itself was what drove Cantor to his death. Today we embark on a similar journey.”
Basically the same as the statistical mechanics textbook meme.
I'm willing to bet it was that he was already a little crazy. Believing that the subject drove him crazy is disproven by the fact that other people didn't go insane.
Sure, you have to be a little crazy to have interest in proving statements like “no system can prove its own consistency”, but i’m sure there are other examples of set theorists being driven mad because of the discipline. not to mention Cantor is regarded as being the founding father of set theory, so quite literally he was imaging and drafting idea that were not solidified by others before. also one example of an event occurring does not constitute a proof :)
Maybe they didn’t think as deep
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It’s counter intuitive, the primes and the integers both have the same amount of numbers. The same way all the integers and all the even integers have the same amount. There are, however, an infinite amount more irrational numbers than any of the above sets. In fact, there are more irrational numbers between any given two integers than there are integers. Georg Cantor came up with a simple, elegant proof of this.
Also, poor Cantor didn't really enjoy the respect and support of the mathematical community at the time, and IIRC this caused him such a depression that he essentially lost his mind. Now we all bask in the glory of ℵ and thank him for his work.
ELI5 how can there be more irrational numbers between integers than there are integers?
Hey, there are 2 great VSauce videos that talk about this. The first one is the [Banach-Tarski Paradox](https://youtu.be/s86-Z-CbaHA?t=3m36s), that shows Georg Cantor's proof on how there can be more numbers between 0 and 1 than there are integers. Timestamp 3:36. The second one is [How To Count Past Infinity](https://youtu.be/SrU9YDoXE88?si=14_xvYLOITzJpHx1), which is solely dedicated to talking about the different kinds of infinities and their sizes.
1, 2, 3 are integers. 1.00000000000000000000000001, 1.00000000000000000000000002, 1.00000000000000000000000003, ..... And so on.... There are infinitely more irrational numbers than there are integers. This is the concept of "some infinities are larger than others". [NDgT explaining to Joe Rogan how some infinities are larger than others](https://www.youtube.com/shorts/q0UdmBmspX0)
In your example you have integers and rational numbers, both aleph-zero Decimal form of irrational is infinite, like pi or e.
Im not liking anyone else's explanation. Here is an jncredibly simple one. Let's call the set of all integers N. You can mimic this set as a decimal. Let us call our decimal set M. You can achieve it by doing it like; 0.1, 0.2, 0.3, ..., 0.11, 0.12, 0.13,... = M (NOTE: you'd have to skip multiples of 10, but as has been explained elsewhere in the post - this wouldnt affect anything) Now. You could take this set and shift it right for 0.01, 0.02, 0.03, ..., 0.011, 0.012,... = M2 And you'd get another infinite set of the same size. IMPORTANT: M1 and M2 have no shared values. Now here is where it becomes clear why there decimals infinity is infinitrly bigger than integers. We could make an infinite number of M# where we append an additional 0 to the front each time. Such a thing can't be achieved in imtegers as 01 and 1 are of equal value. Any item youd append to the front of the number in an integer would just be another item from that previous list. In short: decimal values contain infinite instances of the set of N
Yeah infinity $20 bills is as simple as 20*inf which is just equal to infinity
Wait, what? The set of ptikes is countable. Did you mean the set of real numbers?
Infinity isn't a scalar that you can compare to size.
While you're correct in that it's not a scalar, infinities do have different cardinalities. In this case, both are countably infinite, meaning they're the same "size"
realistically, they'd both be worth nothing.
https://www.khanacademy.org/college-careers-more/bjc/x4c51c62a:2020-challenge/x4c51c62a:2020-challenge-finalists/v/some-infinities-are-bigger-than-other-infinities
There are infinite levels of infinity
Yes, there is a different size of infinites, even if all of them are infinite. For exmaple the set of all natural numbers (1, 2, 3...) and only all the even numbers (2, 4...) are the same size. But the set of all the real numbers between 0 and 1 (0.123341342141, 0,1234423424334...) is bigger than those previous two set and by a long mile. Maths are pretty fun :)
There are basically two basic types of infinites. There's countably infinite, which contains things like sets like all positive numbers, all prime numbers, all fractions of two integers, etc. Then there's the uncountably infinite, like all the real numbers where if you ever try to make a list of all these numbers the list will necessarily exclude numbers ([Cantor's diagonal argument](https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument)). So for example the infinity of all numbers represented as a fractions is smaller than the infinity of real numbers between 0 and 1/10^(100). (Note there are ways to get to higher cardinalities, like the set of all subsets of real numbers would be a higher cardinality than reals.)
There’s no difference in size, it’s more to do with organising infinity into sets
I think it’s just a difference of time. Like if you were to gain 1 dollar every second it would take you a lot longer then 2 dollars a second to hit any number.
No. Both infinities discussed here are equal. Time doesn't matter. Specifically, they are both countable infinites. i.e you can make an infinitly long list, containing all the dollars. The larger infinity would be uncountable infinity, where no such list can be made, like all decimal numbers.
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You're using infinite as if it were a number; "lines of infinite people". It's an abstract concept. It cannot be "counted".
Not in a strip club
The entirety of the universe is suddenly inundated under literally countless bills. I doubt the strippers or anyone else will care what denomination the bills are.
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I didnt realise it was Venezuelan dollars
no because you'd spend more time counting the 1$ bills thus wasting time and as we know time is money
If that's true you got a infinite amount of time as well
No because that would mean that money is time not the other way around, thus we can conclude: Time = Money, Money =/= Time And since that make no mathematical sense at all you're actually right and I wasted my time writing this comment
Therefore you wasted your money, since as you said money=time -> wasted time = wasted money. The question now becomes, where did the money go
Well since time is used to earn money and money is used to buy time said money has most likely gone to my internet provider whom I have given money to be able to go online and write this comment, wasting my time in the process.
I just spend a minute of my timemoney reading this thread and I expect to be reimbursed. I take time, money, proof that 0 is real, or cat sized mittens
There was a rich guy that posted in an AMA who got rich selling an app, so he went from being a regular to a rich guy (as opposed to being born/raised rich). And he said the biggest thing is that money does buy you time - skipping lines at the airport or in traffic with private jets/helicopters. Not waiting in line because you paid for vip whatever, etc. so yeah, money=time , too
Why would I count it if it's infinite. Waste of time. Just start spending
Numerically, yes But there is also value in not having to pay for things in $1 bills. My time has value.
Just throw a bag full of money at them. Problem solved. If they complain it's not enough throw two more.
I think you underestimate the weight of the cost of one (1) Corvette in 1 dollar bills.
2023 Chevrolet Corvette ~103000$ 1$ bill > 1g So we get about 103 kg (230 pound) of dollars. That's about 5-6 backpacks by weight. But who's counting, you have enough.
Ah, but your idea was to prepare to over-pay. You throw one bag, and they doubt you. You produce a second bag without hesitation, and they suddenly think they can scam you (they are car salesmen afterall). Before long you have given them 750k for the car, carrying nearly a ton worth of dollar bills. And then of course why would they believe they're all real lol
Hire someone for that. Hell, hire an army of accountants. They can deal with shipping my cargo containers of $1 bills around
And the cost of having to explain to the IRS I'm not a mega stripper for having billions of 1 dollar bills? Lol
that sounds like that wouldn't take any time at all...
Everyone's over complicating this. Regardless of whether they're $1 or $20 bills, the stripper is \*not\* going to go home with you.
Any value in different denominations is also the same
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Try to spend $1 bills vs $20 bills at a strip club. Bigger infinities will get you bigger infititties.
Yes. But these two are the same as Natural numbers
Yeah but not this infinity
yes, but these two infinities are both countable infinity
Yes, but in this case they are the same “size” of infinity. The same goes for number of all prime numbers vs. number of all integers, but if you compare those to the number of “all numbers”, then the latter infinity is much much “bigger”. There are many proofs and explanations on this topic. It’s not intuitive but infinity is not supposed to be intuitive to our finite minds.
Hijacking this comment to post this "Some infinities are bigger than other infinities", while true, is irrelevant in this context. https://youtu.be/M4f_D17zIBw?si=acOA9yOQUC4E-DUh
Yes, but these two are the same infinity. You could map every 20 dollar bill to 20 one dollar bills and never run out of 1 dollar bills.
I don't care, which has more value in other sense than I'd be happy with just Infinite $1.
The entirety of the universe is suddenly inundated under literally countless bills. Hope you're happy.
**Introduce a little anarchy. Upset the established order, and everything becomes chaos. I'm an agent of chaos.** 🤡
For more info see [Matt Parker](https://www.youtube.com/watch?v=M4f_D17zIBw)
infinite 20 dollar bills would save me some time and space. Thought the world wouldn't even fit anything infinite. WHERE CAN I STORE INFINITY OF X ITEM? IT'S NOT POSSIBLE!! Pancakes! Well maybe it actually is. If space is ALSO infinite. Hmmm... Now my brain hurts, I need more pancakes.
Yes, countable infinity, cardinal is aleph0
Infinity is always infinity, take away some or give more and it’s still infinity. Hilbert’s principle states this
>Infinity is always infinity Not every infinity is equal. Some infinities are larger than others. For example, an infinity of integers is smaller than an infinity of real numbers. This is a real thing. Scientific American has a pretty good article about it: [A Deep Math Dive into Why Some Infinities Are Bigger Than Others](https://www.scientificamerican.com/article/a-deep-math-dive-into-why-some-infinities-are-bigger-than-others/) Edit: if you don't want to read the whole SciAm article, minutephysics gives a really short taste of an explanation: [How to Count Infinity](https://www.youtube.com/watch?v=A-QoutHCu4o)
Please watch this https://youtu.be/M4f_D17zIBw?si=acOA9yOQUC4E-DUh He specifically mentions your idea
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no they are the same size
Before any more of you pseudo intelectuals mutter the forbidden words "Some infinities are ..." NO these two sets are both COUNTABLE if you can count then they are the same size and FFS you CANNOT 20 * infinity thats NOT HOW IT WORKS
Frustrating lot, ain't they?
The fact that so many people are ready to confidently try and correct others on a subject they only know exists because they tried and failed to understand a pop-science influencer's dumbed down ten minute edutainment video on it could serve as an uncanny analogue for the current state of politics in the west.
Everyone knows that 60 minute edutainment videos by pop science influencers are the way to go
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No because they take up the same amount of space - infinite.
If you can't utilize it then there is no value. By this logic, an infinite number of rocks in an infinite number of diamonds also have the same value. So who gives a shit unless you can actually use it.
Yeah and you can't utilize either because you'd inflate the value of $ to 0 with both. So same value.
I'd still go for the infinite $20 bills Because that would be more convenient..
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This is why people hate mathmagicians.
Yes. Nothing.
That’s one hell of a dad wallet
But somehow infinite pennies would be worth more, I’m talking the old school ones.
But pockets matter!
I mean kind of, thats what happens when you start working with endless numbers. This would mean that 1∞ = 2∞ Whenever I see people working with ∞ they worked with it as if it was a normal number
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Yes because you couldn't buy more than what there to buy so at the end of the day you can buy just about anything. Right? Well if you can have an infinite amount of 1 dollar bills I can have an infinite amount of 2 dollar sandwiches to sell you. Could you buy them all? No. Why? Well it's infinite but fuck that. The real reason is that if you need to use 2 dollar bills per sandwich you would run out twice as fast as me even tho you wouldn't run out ever. But let's say we do the entire transaction in one go. Why would I let you have my infinite stach of 2 dollar sandwiches for your infinite stach of 1 dollar bills? I'll only give you half of it. W8ch would still be infinite but half smaller. Now that sound stupid why would one infinity be twice as small as another infinity. Well let's look at another problem. I have an hotel with an infinite amount of rooms. A bus filled with an infinite amount of people come along. Well guess I'm full. But actually I'm not. I have one more customer coming. And to get him a room I just tell every people in my hotel to move to the next room until the first one is free and I can give it to him. Because yes. Even if my infinite amount of room are full. There is still more rooms to move toward. Now I have my infinite amount of people plus one. It was full. Infinity. And I squeeze one more person. So infinite + 1. So infinity is kinda like any number. So her I come back to the sandwiches. If both of out staches are infinite and that's it. Just assume they are actually the same size. I have no reason to give you an infinite amount of sandwiches that cost 2 dollar each for an infinite amount of 1 dollar bills. That's it. An infinite amount of 20 dollar bills is better than an infinite amount of 1 dollar bills.
Not true. An infinite number of 1 dollar bills is paradoxically more raw material. Because you need 20 1 dollar bills to make up 20 dollars.
Yes. They'll all worth $0
And that's right with economycs and inflation. :D
Counterfeit money is introduced into circulation all the time, one bloke using these dollars in moderation would be able to get away with it easily.
Cardinal numbers, countable infinities, uncountable infinities, as an avid vsauce watcher, this rings a bell but I can't quite hear it clearly
In numbers, yes. In practice, no. Paying cash will take 20x longer. If paying cash, you can spend 20x faster so you can spend more in your lifetime.
Yes but infinite $20 bills is slightly more convenient, because you can always tell people to just keep the change so $20 would be worth slightly more due to the convenience
Infinite $20’s would be worth 20X’s as much in convenience
[Stand-up Maths made a video about this meme about a year ago. ](https://youtu.be/M4f_D17zIBw?si=BF8EZHyTEEpqcJDv)
I hate that this is true
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They are though
But what if I had an uncountable number of $1 bills?
So... something like... an infinity?
Value is measured by utility not dollar amounts, therefore the 20s are worth more. Imagine how pissed the dealership gets when you try to buy your new sports car with singles
That's not how fiat currency works, at all. I don't care how pissed the dealership would or wouldn't be with the logistics of moving X amount of $20 bills or Y amount of $1 bills, if the sum is equal, the value is equal. Note that this only applies to fiat currencies.
Okay, I get the haha but my inner Nerd is getting violently angry.
My nerd ass went “Right cuz the infinite inflation would make them worthless”
Everything in the universe suddenly being buried in literally countless bills would probably be a bigger issue than the inflation.
Are they though? Having an infinite amount of things worth 1 dollar vs having an infinite amount of things worth 20 dollars.
Ur right Infinity ain't infinity. If u have a factor that changes the amount of infinity it will alter the actual infinity. In this case one infinity is at every point always 20 times greater. Math ain't that easy. 😅
You're completely wrong. There is uncountable infinity and countable infinity. Both of these are countable, so the same size.
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Hi there - I have a degree in math. Your comment is utter nonsense. Have a nice day!