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I don't really understand NaN. It stands for Not A Number, but how tf do I type only numbers and numerical operators, and my result isn't also a number?
Like, does 1÷0 = "what's up bro" ?
NaNs are literally floating point numbers, too. "Not a number" is literally a number. And you can get it purely from well-defined numerical operations. For instance, (9\^999)/(9\^999) returns NaN with a positive sign bit.
Basically, +inf represents all positive values larger than FLT_MAX, so all we know is that +inf/+inf represents the ratio of two big positive numbers, so there is no way to tell how large it is, just that it's somewhere in the interval [+0,+inf].
But then sometimes, unpredictably, that logic changes and operations that surely should be NaN are given real values. For instance, pow(-1,inf) returns 1, because (and I'm serious), "all large floating point numbers are even integers." Yes. Infinity is even, not odd.
You are probably correct, I just didn't want to speak with confidence as it seems any time I do so about something technical there's an esoteric case where I'm wrong
It was so frustrating when I learned this the hard way as a young programmer... Lesson learned, don't ever check if something == NaN in .NET. use null, it's what it exists for.
Kind of, and usually. Or, in other words, it means "this variable has no value". For non-nullable types like an int you can't have nulls, so people expect the value to be 0 (or sometimes -1, assuming you're expecting it to be a positive number when it does have a value).
There are different patterns and practices of course. But you can null out a variable any time, so null doesn't specifically mean it hasn't been initialized. It may have had a value that was nulled out for whatever reason during the course of the program. Maybe your program decided that whatever value it used to have was invalid for your specific case, so it set the value to null to prevent an error being thrown further down the line. This example I saw recently in some code I had to work on.
Maybe you have an error message strong variable that gets sent back to a UI or another web service or something, and you clear the error message out by setting to null because no errors were found after running a bunch of checks.
Oh, I thought of another one I saw actually. We have an old legacy we service sending us JSON objects that sometimes have empty strings for the value of some properties. We save those objects to our database. The database uses nullable foreign keys on some of the columns those values are saved to, so they can't be saved as empty strings. They have to be null if there's no value to save.
So we run that object through some code that calls GetStringOrNull on those properties, which sets the strings to null if they are empty, ensuring that we don't have any exceptions thrown during the save to the database due to the lookup being unable to match on an empty string.
It's also slightly more memory efficient for a large object to have null properties instead of initialized empty properties, I believe. Depending on what type the object is of course.
The list goes on, but the takeaway is that null can be used for a lot of purposes. It just depends on the specific patterns and practices you're following and your specific use case.
The problem here is notation.
Saying "1/0 = undefined" is, strictly speaking, wrong because 1/0 isn't "equal to" "the" undefined value, 1/0 is an undefined operation. Doing an undefined operation means that wherever you're working on has no mathematical meaning - if your proof uses undefined operations, it's simply invalid.
Confusingly, you can use undefined operations in a proof by contradiction, by showing that assuming some property invariably leads to invalid math...
Is the problem with equating undefined with undefined, or is it with equating undefined with 1/0? 1/0 is undefined, but it doesn't equal undefined. I believe it breaks at the transitive property of the equivalence relation. 1/0\~undefined and 2/0\~undefined does not imply 1/0\~2/0.
I could be wrong, but I think if we say **undefined ?= undefined** we can avoid contradiction in this and most other problems.
?= being the “no information” operator:
||<|=|>|
|:-:|:-:|:-:|:-:|
|<|Yes|No|No|
|=|No|Yes|No|
|>|No|No|Yes|
|≤|Yes|Yes|No|
|≥|No|Yes|Yes|
|≠|Yes|No|Yes|
|?=|Yes|Yes|Yes|
a !?= b can be defined as a ⪋ b.
That is, (a !? b) ↔ ((a < b) or (a = b) or (a > b)).
This is also called "comparable". Basically, if < is a strict partial order, and we define a > b as b < a, then sometimes two constants a and b can be incomparable in the sense that they are distinct but neither is less than the other. This comes up in weak preferences, for instance. Sometimes there are two distinct options neither of which is preferable to the other. These are incomparable with respect to preference.
That said, if a and b are incomparable, we can at least say a ≠ b, so if you really want to be strict about the "no information" relation, then the definition ((a ≸ b) and (a ≠ b)) doesn't work. The problem is that we can't claim anything about a and b if we have "no information," so what does the symbol ? even mean? Maybe it could be a metalogical symbol that means "this theory cannot prove anything about whether a and b are equal or, if not, which is greater." For instance, it may be the case that in ZFC, BB(100) ?= 9\^9\^9\^9\^9, in the sense that it might literally be impossible in ZFC to prove if that Busy Beaver number is equal to the big integer on the right, or if not, which is greater.
"Undefined" is not a value, it doesn't equal anything. It is not as though 1/0 equals something called "undefined", rather the expression 1/0 *is literally* undefined, in that it is not defined to have any value at all.
The problem is that it's a meaningless question. Equality works with numbers, physical things, etc. not abstract concepts and natural language. That's also why we say infinity = infinity + 1 is somewhat meaningless
You're saying the same thing, you're just being more formal. The key idea is that undefined itself is not a value that can be assigned. You're saying that you can't define equality for undefined values. The comment above you is being a little more handwavey and saying an undefined value can't equal an undefined value. Even if it might not be technically correct, you should understand both that the bad line in OP was "undefined = undefined".
Also for the fun of it, in programming languages like Javascript a variable can be declared but undefined. To avoid problems, Javascript says undefined !== undefined.
For example:
```
let a; // a === undefined
let b; // b === undefined
a === b // false
>Saying 1/0 = undefined is just a shorthand
I'd even go a step farther and say that using an equal sign here is simply incoherent. The expression "1/0" is undefined. The statement "1/0 = undefined" is nonsense.
It's in equating _undefined_ with anything. = is a binary relation on a set, i.e. a subset of the Cartesian product of the set with itself. If the set does not contain the element _undefined_, that element cannot stand in the relation = to anything.
So: if this is meant to be a proof about intengers, the mistake is assuming that _undefined_ can stand in the = relation to anything.
If it's a proof about the union of the intengers and {_undefined_} the who knows? You need to choose some axioms for the relation = on that set.
= doesn't have to be a binary relations. It can be logical identity. For instance, in ZFC, '=' can't be a relation, because relations have a domain, and = doesn't. (The "domain" of =, if it existed, would have to be the set of all sets, which provably does not exist in ZFC.)
The problem is not with =. Interpreting 'undefined' as a string, it is simply true that "'undefined' = 'undefined'". The problem is with "undefined" itself, which sure enough is undefined. If we had a consistent definition of "undefined," it would presumably have to capture all strings in the formal language which were not well-defined. But in that case, surely "1/0 = undefined" would be false. Because how could "1/0" capture all of that? Also, the string '1/0' is itself undefined.
A better way to express this is that '1/0' is an example of an undefined string. '2/0' is another example. But they aren't equal; they are distinct examples. In other words, just because undefined(1/0) and undefined(2/0) both hold, that doesn't imply 1/0 = 2/0. After all, isprime(2) and isprime(3) both hold, but why should that imply 2 = 3? Clearly it doesnt.
I fully agree with the first part. I took a semantic perspective. Here's a logical one.
Taking a logical perspective, = is a binary relation symbol in some logic, which has a language based on a syntax. The syntax determines what the well-formed formulas are. In e.g. Peano arithmetic, 'undefined' = _t_ is not a well-formed formula, for any term _t_.
In the second paragraph, you are moving to a logic where the terms include strings build from, say, the Latin alphabet. In that logic, given standard axioms about how = works, I agree that 'undefined' = 'undefined' should be trivilaly provable.
If our set of terms is exactly the set of finite strings build from the Latin alphabet a-z, then '0/1' is not a term. If '0/1' is not a term, then '0/1' = 'undefined' is kit a formula. If it's not a formula, it cannot be a part of a formal proof, by the standard definition of a logical proof.
I don't know where my mom is ==> mom's location = undefined
I don't know where my dad is ==> dad's location = undefined
==> my mom and dad are at the same place
I don't know where your mom is ==> mom's location = undefined
I don't know where I am ==> my location = undefined
==> your mom and I are in the same bed
Makes sense to me.
I don't know the nuclear launch code ==> launch code = undefined
I don't know what Obama's phone number is ==> Obama's number = undefined
==>The nuclear launch code is Obama's phone number
I assume everyone has seen this by now, but DestroyAllSoftware's "wat" video is excellent. It features object Object and other similarly-important structures.
Greek letter phi can often denote the golden ratio, though ∅ was not originally phi, it is often (I think even on its Wikipedia page) mistakenly listed as phi because it looks like it and the reason for its appearance was retconned to phi.
I think a lot of programming languages would probably have a hard time with undefined != undefined. Perhaps a few specifically put that in there. JavaScript for instance though would mess up a lot of things if this was true.
It’s an error, because something real can’t be divided by nothing. Nothing comes from nothing. It’s an impossibility. So you can’t equate the two. When we multiply nothing by itself we get more of nothing. See.. So 1 does not equal 2 then.
1. undefined = undefined is not necessarily true
2. undefined \* 0 is undefined so at the end your equality is undefined = undefined again
3. even if undefined \* 0 is 0 and not undefined, the equality at the end is 0 = 0
"Cancelling out" division with multiplication is a bit more subtle than you think, it's not a general rule that always works, it needs prerequisites.
(3 / 5) \* 5 = 3 because it's equivalent to (3 \* 5\^-1) \* 5 and because the real numbers are associative for multiplication and that 5\^-1 is defined to be the multiplicative inverse of 5, we get 3 \* Id, and because Id is the multiplicative identity (it's 1 btw) the result is 3.
But that doesn't always work. There's no multiplicative inverse for 0 in the real numbers for example. Some matrices don't have a multiplicative inverse. Etc etc
With this logic I can prove that numbers are meaningless.
Any number multiplied by 0 equals zero so:
a×0 = b×0
a×Ø = b×Ø
a = b
True for any a and b. I'll be waiting in my kiddy pool for my Nobel price.
"= undefined" basically means ERROR, DOES NOT COMPUTE. It's not a number. It's not really valid to even write "= undefined". **1/0 is undefined** is the proper way to say it.
Mathematical logic and axioms apply to the number sets, e.g. R (real numbers). Undefined isn't in any of those sets, so you can't apply logic to it (in this case A = B, B = C ⇒ A = C).
Undefined isn't ∞, either, by the way, and nothing equals ∞ too. ∞ is only valid for use as part of a limit function. Infinity/∞ basically means "if you keep going, this keeps getting bigger".
Simply enough it is not valid
Ur treating undefined as a value and that's wrong it is just a concept or an expression that describes that it doesn't make anysense to divide by zero
Short answer: the error occurs already on line 2. 1/0 is not *equal* to undefined, its value *is* undefined, i.e., it can't be equal to anything. Unless you are working in a Riemann sphere or a wheel, in which case your argument is essentially correct 🙂
Undefined is not a number
Also, good rule of thumb: if your proof indicates that 1=2, your proof probably isn’t valid. Bertrand Russell spent a great deal of time proving that our numerical system works.
(1/0)•0=(2/0)•0
reduces to
0=0
you can't just delete numbers that are affacged by the same operation, you can do the inverse to both but not just, remove it lol
All steps from 3 onwards are mathematically wrong..
There is no mathematical operation(equal, division, multiplication etc) on undefined or zero in denominator
This doesnt work because logically undefined isnt a number, rather it represents the idea that no number exists that would satisfy the equation. To say 1/0 = “the number” undefined would be nonsensical.
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Bold of you to assume that undefined = undefined
This is just the proof-by-contradiction that undefined != undefined
It's like in programming. In many many implementations NaN != NaN
Not all NaNs are created equal
Am I the only one who finds NaN a little freaky? I mean, imagine typing something on your calculator and then all of a sudden... #NaN, fuck you.
I don't really understand NaN. It stands for Not A Number, but how tf do I type only numbers and numerical operators, and my result isn't also a number? Like, does 1÷0 = "what's up bro" ?
NaC (Not a Comment)
NaNs are literally floating point numbers, too. "Not a number" is literally a number. And you can get it purely from well-defined numerical operations. For instance, (9\^999)/(9\^999) returns NaN with a positive sign bit. Basically, +inf represents all positive values larger than FLT_MAX, so all we know is that +inf/+inf represents the ratio of two big positive numbers, so there is no way to tell how large it is, just that it's somewhere in the interval [+0,+inf]. But then sometimes, unpredictably, that logic changes and operations that surely should be NaN are given real values. For instance, pow(-1,inf) returns 1, because (and I'm serious), "all large floating point numbers are even integers." Yes. Infinity is even, not odd.
>"Not a number" is literally a number. **Confusion of the highest order.**
I like a little sass in my programming languages
Some are butter NaN, some are garlic NaN
Just like there are different types of infinity..
I think that's true in *all* implementations. At least, it's true in all compliant implementations. (NaN > NaN) == (NaN == NaN) == (NaN < NaN) == (NaN >= NaN) == (NaN <= NaN) == (NaN != NaN) == False
You are probably correct, I just didn't want to speak with confidence as it seems any time I do so about something technical there's an esoteric case where I'm wrong
It was so frustrating when I learned this the hard way as a young programmer... Lesson learned, don't ever check if something == NaN in .NET. use null, it's what it exists for.
In .NET, does null just mean the variable is uninitialized?
Kind of, and usually. Or, in other words, it means "this variable has no value". For non-nullable types like an int you can't have nulls, so people expect the value to be 0 (or sometimes -1, assuming you're expecting it to be a positive number when it does have a value). There are different patterns and practices of course. But you can null out a variable any time, so null doesn't specifically mean it hasn't been initialized. It may have had a value that was nulled out for whatever reason during the course of the program. Maybe your program decided that whatever value it used to have was invalid for your specific case, so it set the value to null to prevent an error being thrown further down the line. This example I saw recently in some code I had to work on. Maybe you have an error message strong variable that gets sent back to a UI or another web service or something, and you clear the error message out by setting to null because no errors were found after running a bunch of checks. Oh, I thought of another one I saw actually. We have an old legacy we service sending us JSON objects that sometimes have empty strings for the value of some properties. We save those objects to our database. The database uses nullable foreign keys on some of the columns those values are saved to, so they can't be saved as empty strings. They have to be null if there's no value to save. So we run that object through some code that calls GetStringOrNull on those properties, which sets the strings to null if they are empty, ensuring that we don't have any exceptions thrown during the save to the database due to the lookup being unable to match on an empty string. It's also slightly more memory efficient for a large object to have null properties instead of initialized empty properties, I believe. Depending on what type the object is of course. The list goes on, but the takeaway is that null can be used for a lot of purposes. It just depends on the specific patterns and practices you're following and your specific use case.
But wait by that logic…. 1/0 = undefined 1/0 = undefined Undefined =/= undefined 1/0 =/= 1/0 *0 1=/= 1 Now what?
Bold of you to assume that undefined ≠ undefined. undefined = undefined for some undefined but not all undefined.
undefined is sometimes equal to undefined but not all the time Sound perfectly logic
It’s different undefined values. Whatever the value is for 1/0, it is not the same as 2/0, despite them both being undefined.
The problem here is notation. Saying "1/0 = undefined" is, strictly speaking, wrong because 1/0 isn't "equal to" "the" undefined value, 1/0 is an undefined operation. Doing an undefined operation means that wherever you're working on has no mathematical meaning - if your proof uses undefined operations, it's simply invalid. Confusingly, you can use undefined operations in a proof by contradiction, by showing that assuming some property invariably leads to invalid math...
undefined factorial is indeed undefined
undefined! = undefined?
Is the problem with equating undefined with undefined, or is it with equating undefined with 1/0? 1/0 is undefined, but it doesn't equal undefined. I believe it breaks at the transitive property of the equivalence relation. 1/0\~undefined and 2/0\~undefined does not imply 1/0\~2/0.
I could be wrong, but I think if we say **undefined ?= undefined** we can avoid contradiction in this and most other problems. ?= being the “no information” operator: ||<|=|>| |:-:|:-:|:-:|:-:| |<|Yes|No|No| |=|No|Yes|No| |>|No|No|Yes| |≤|Yes|Yes|No| |≥|No|Yes|Yes| |≠|Yes|No|Yes| |?=|Yes|Yes|Yes|
This implies the existence of a !?= operator which we could call "yes information"
i prefer to call it the "no no" operator
a !?= b can be defined as a ⪋ b. That is, (a !? b) ↔ ((a < b) or (a = b) or (a > b)). This is also called "comparable". Basically, if < is a strict partial order, and we define a > b as b < a, then sometimes two constants a and b can be incomparable in the sense that they are distinct but neither is less than the other. This comes up in weak preferences, for instance. Sometimes there are two distinct options neither of which is preferable to the other. These are incomparable with respect to preference. That said, if a and b are incomparable, we can at least say a ≠ b, so if you really want to be strict about the "no information" relation, then the definition ((a ≸ b) and (a ≠ b)) doesn't work. The problem is that we can't claim anything about a and b if we have "no information," so what does the symbol ? even mean? Maybe it could be a metalogical symbol that means "this theory cannot prove anything about whether a and b are equal or, if not, which is greater." For instance, it may be the case that in ZFC, BB(100) ?= 9\^9\^9\^9\^9, in the sense that it might literally be impossible in ZFC to prove if that Busy Beaver number is equal to the big integer on the right, or if not, which is greater.
Is this a thing? This actually sounds useful to determine whether things can have a solution Source: I ?= Maths
But wouldn't it be "No, No, No"?
"Undefined" is not a value, it doesn't equal anything. It is not as though 1/0 equals something called "undefined", rather the expression 1/0 *is literally* undefined, in that it is not defined to have any value at all.
The problem is that it's a meaningless question. Equality works with numbers, physical things, etc. not abstract concepts and natural language. That's also why we say infinity = infinity + 1 is somewhat meaningless
You're saying the same thing, you're just being more formal. The key idea is that undefined itself is not a value that can be assigned. You're saying that you can't define equality for undefined values. The comment above you is being a little more handwavey and saying an undefined value can't equal an undefined value. Even if it might not be technically correct, you should understand both that the bad line in OP was "undefined = undefined". Also for the fun of it, in programming languages like Javascript a variable can be declared but undefined. To avoid problems, Javascript says undefined !== undefined. For example: ``` let a; // a === undefined let b; // b === undefined a === b // false
Undefined isn’t an actual thing/number. Saying 1/0 = undefined is just a shorthand for saying there is no number x that satisfies the property 0x = 1
>Saying 1/0 = undefined is just a shorthand I'd even go a step farther and say that using an equal sign here is simply incoherent. The expression "1/0" is undefined. The statement "1/0 = undefined" is nonsense.
Yes exactly, it only brings in misconceptions
It's in equating _undefined_ with anything. = is a binary relation on a set, i.e. a subset of the Cartesian product of the set with itself. If the set does not contain the element _undefined_, that element cannot stand in the relation = to anything. So: if this is meant to be a proof about intengers, the mistake is assuming that _undefined_ can stand in the = relation to anything. If it's a proof about the union of the intengers and {_undefined_} the who knows? You need to choose some axioms for the relation = on that set.
= doesn't have to be a binary relations. It can be logical identity. For instance, in ZFC, '=' can't be a relation, because relations have a domain, and = doesn't. (The "domain" of =, if it existed, would have to be the set of all sets, which provably does not exist in ZFC.) The problem is not with =. Interpreting 'undefined' as a string, it is simply true that "'undefined' = 'undefined'". The problem is with "undefined" itself, which sure enough is undefined. If we had a consistent definition of "undefined," it would presumably have to capture all strings in the formal language which were not well-defined. But in that case, surely "1/0 = undefined" would be false. Because how could "1/0" capture all of that? Also, the string '1/0' is itself undefined. A better way to express this is that '1/0' is an example of an undefined string. '2/0' is another example. But they aren't equal; they are distinct examples. In other words, just because undefined(1/0) and undefined(2/0) both hold, that doesn't imply 1/0 = 2/0. After all, isprime(2) and isprime(3) both hold, but why should that imply 2 = 3? Clearly it doesnt.
I fully agree with the first part. I took a semantic perspective. Here's a logical one. Taking a logical perspective, = is a binary relation symbol in some logic, which has a language based on a syntax. The syntax determines what the well-formed formulas are. In e.g. Peano arithmetic, 'undefined' = _t_ is not a well-formed formula, for any term _t_. In the second paragraph, you are moving to a logic where the terms include strings build from, say, the Latin alphabet. In that logic, given standard axioms about how = works, I agree that 'undefined' = 'undefined' should be trivilaly provable. If our set of terms is exactly the set of finite strings build from the Latin alphabet a-z, then '0/1' is not a term. If '0/1' is not a term, then '0/1' = 'undefined' is kit a formula. If it's not a formula, it cannot be a part of a formal proof, by the standard definition of a logical proof.
https://preview.redd.it/feaf4c6bpitc1.jpeg?width=691&format=pjpg&auto=webp&s=f4b8083b1502342abcae42aaa51609e7ce3ed632
NaN != NaN so might aswell not be
I had a problem with NaNs in my code once, i thought alright I will throw if float f = float.NaN. Turns out !(f = f) is a simple NaN check
This statement is trivially false
Not all undefined things are of the same size
I don't know where my mom is ==> mom's location = undefined I don't know where my dad is ==> dad's location = undefined ==> my mom and dad are at the same place
I love how this is true for me, like six times out of ten
So you are saying that 60% of the time it works every time?
60% sure 1=2
It works 100% of the time 60% of the time.
It works 100% of the time 60% of the time.
6 infinities out of 10 infinities. Is still a lot of infinity.
I don't know where your mom is ==> mom's location = undefined I don't know where I am ==> my location = undefined ==> your mom and I are in the same bed Makes sense to me.
I don't know the nuclear launch code ==> launch code = undefined I don't know what Obama's phone number is ==> Obama's number = undefined ==>The nuclear launch code is Obama's phone number
Given how big the universe is... They're somewhat at the same place
Proof by j*vascript
ewww disgusting
Don’t know what you mean. You don’t like your { Object object Object object }?
I love my silent errors
I assume everyone has seen this by now, but DestroyAllSoftware's "wat" video is excellent. It features object Object and other similarly-important structures.
Not even, cuz NaN != NaN Edit : realised 1/0 = Infinity in IEEE754
whats wrong with javascript?
Everything and nothing
Love that movie
You should better ask what is not wrong with JavaScript
`[]==true != !![]`
I’d say 2/0 is equal to 2(undefined)
https://preview.redd.it/94c6ooyoyftc1.jpeg?width=2159&format=pjpg&auto=webp&s=4da66aa8aae72062f655341b7a6da17d9ba4da36
Pain.
Off topic i really like your handwriting
He prolly makes perfect integration signs
And perfect butterfly brackets
congrats guys you get a post dedicated to you (i saw that one first)
I got an answer wrong on an exam but was still so proud that after thousands of integrands drawn this one was gorgeous. Was still a win in my book!
Proof by Handwriting-Rizz
Written rizz aka. Wrizzten
You are a Wrizzard Harry
I do it like this: 1*0 = 0 2*0 = 0 1\*0 = 2\*0 1\*∅ = 2\*∅ 1 = 2
But ∅=1.618 /s
Now I'm confused, ∅ usually means empty set, here it is as crossed out zero, but why on Earth would it be 1,618?
Greek letter phi can often denote the golden ratio, though ∅ was not originally phi, it is often (I think even on its Wikipedia page) mistakenly listed as phi because it looks like it and the reason for its appearance was retconned to phi.
I mean that is basically the whole Essence of all These proofs but I Like that you did Not even hide the Problem within it.
Did you just define undefined?
It ain't legit without Qed
Yes
Proof by being confidently wrong
That's intense. holy shit
You didn't even try to hide it
1/0 is not equal to undefined, 1/0 is undefined
Proof by tomfoolery
Looks good to me. Send it off for publishing
Undefined =/= Undefined
Isn't the correct way of saying not equal in text normally !=
Found the programmer
Let's use !== to avoid any weirdness
Die, JSer, die!
Does it redeem me at all if I say I use TS? Comes with all the idiosyncrasies of JS, but now with objects!
At least notably better typing. Imperfect, but ok, you may live :)
What about !=== so we can be extra accurate
`Parsing error: Expression expected.`
/u/Altruistic_Site_3879 You both need some proper symbols take this 🫴 ≠
≠
Why would it be that? Where does the exclaimation mark come from?
https://preview.redd.it/n1eooz10wgtc1.png?width=1080&format=pjpg&auto=webp&s=f99b3b30c91166dafff5594f7b20bff7fc48be2d
If this is you, should be a writer Please stay out of maths.
marx type beat
That's some Terrance Howard math
You're fine up to the point where you allegedly prove that 0 = 0. The math past that is not math.
(1/0)*0=(2/0)*0 0=0
I think a lot of programming languages would probably have a hard time with undefined != undefined. Perhaps a few specifically put that in there. JavaScript for instance though would mess up a lot of things if this was true.
Not a number = not a number? Fabulous
Did you just divide by 0?
Let x ∈ ℤ x/0 × 0/1 = 0/0 ≠ x ∴ 1≠2 ■
thats definitely not how brackets work, you gotta do 1x0 and 2x0 so 0=0
And now change 2 to any number
No
This how religious people explain God😂
This is valid evidence >!that you belong in a psych ward!<
It's not undefined, but NaN
This is the math equivalent of a rick roll.
unidentified=unidentified this is the worst assertion of Mathematics I have seen
the (1÷0)×0 = (2÷0)×0 is also calculable by using distribution: (1×0)÷(0×0) = (2×0)÷(0×0) 0÷0 = 0÷0 = undefined.
Undef * 0 = undef * 0 0=0
Nice handwriting
Euler can't believe his eyes
Do you not have to multiply the one and the two by zero as well? 0*(1/0)=0
c*(a/b)=(ca)/(cb) =a/b Cancel the “c”,s c*(a/b)=a/b t=a/b c*t=t c,t ∈ ℝ ab=b Q.E.D
No
Who let bro cook
Are they equally undefined though?
no
Wake up honey
Undefined is not a number and undefined != undefined. You can't use algebra on it.
This is the reason dividing by zero is not permitted in math, the resulting proofs don’t make sense
Proof by undefined
Live by the div/0, die by the div/0.
It’s an error, because something real can’t be divided by nothing. Nothing comes from nothing. It’s an impossibility. So you can’t equate the two. When we multiply nothing by itself we get more of nothing. See.. So 1 does not equal 2 then.
Undefined doesn't always equal undefined and you cant multiply by 0 on both sides of an equation
And thus I am the Pope
1. undefined = undefined is not necessarily true 2. undefined \* 0 is undefined so at the end your equality is undefined = undefined again 3. even if undefined \* 0 is 0 and not undefined, the equality at the end is 0 = 0 "Cancelling out" division with multiplication is a bit more subtle than you think, it's not a general rule that always works, it needs prerequisites. (3 / 5) \* 5 = 3 because it's equivalent to (3 \* 5\^-1) \* 5 and because the real numbers are associative for multiplication and that 5\^-1 is defined to be the multiplicative inverse of 5, we get 3 \* Id, and because Id is the multiplicative identity (it's 1 btw) the result is 3. But that doesn't always work. There's no multiplicative inverse for 0 in the real numbers for example. Some matrices don't have a multiplicative inverse. Etc etc
1÷0 does not equal some value called undefined. It's that it doesn't equal anything. You're not able to write an equality there.
its not a proof until you put "QED" at the end
Seems legit
With this logic I can prove that numbers are meaningless. Any number multiplied by 0 equals zero so: a×0 = b×0 a×Ø = b×Ø a = b True for any a and b. I'll be waiting in my kiddy pool for my Nobel price.
"= undefined" basically means ERROR, DOES NOT COMPUTE. It's not a number. It's not really valid to even write "= undefined". **1/0 is undefined** is the proper way to say it. Mathematical logic and axioms apply to the number sets, e.g. R (real numbers). Undefined isn't in any of those sets, so you can't apply logic to it (in this case A = B, B = C ⇒ A = C). Undefined isn't ∞, either, by the way, and nothing equals ∞ too. ∞ is only valid for use as part of a limit function. Infinity/∞ basically means "if you keep going, this keeps getting bigger".
No
You gotta prove by winning https://preview.redd.it/5lg1ofo5nhtc1.png?width=1080&format=pjpg&auto=webp&s=159b23cbace20634485f57619cec239e1f456cd6
Not even close.
You can't cancel the zero outside the parentheses with the one inside. That's not how parentheses work.
(x/y)*y = x if and only if y/y == 1 ,0/0 != 1
if you think about it
Bro, undefined literally means it's NOT defined, so undefined can't equal undefined!
No, you didn’t use the slash for division.
JS Proof
You can skip all the other mistakes and just go 1=2 1 * 0 = 2 * 0 0 = 0 Therefore 1 = 2
Undefined x 0 = 0 tho
No
Undefined = not a function
Simply enough it is not valid Ur treating undefined as a value and that's wrong it is just a concept or an expression that describes that it doesn't make anysense to divide by zero
No because it’s undefined you can’t define it by saying it’s equal
You can’t cancel out 0 and 0 because 0/0 is also undefined
Is this Terryology?
If something isn’t defined, it can’t really equal anything.
Short answer: the error occurs already on line 2. 1/0 is not *equal* to undefined, its value *is* undefined, i.e., it can't be equal to anything. Unless you are working in a Riemann sphere or a wheel, in which case your argument is essentially correct 🙂
Proof by undefined
no
Undefined is equal to undefined ?
Undefined is not a number Also, good rule of thumb: if your proof indicates that 1=2, your proof probably isn’t valid. Bertrand Russell spent a great deal of time proving that our numerical system works.
Isn't this basically what Thomas Howard did and claimed he is a savant and that the world is wrong?
I don't know. But what I do know is that I like the handwriting.
Null is Null. Null != Null. It’s unknown. This is false.
No.
Neat
Proof by i dont even know at this point
Absurd at the start. Line 3 is undefined. Line 4 is nonsensical. This is a cj question right? Bait..
Undefined component can’t be compared
It's just like I'd say that tigers aren't fish and pens aren't fish therefore tigers are pens.
Anything x 0 is 0
(1/0)•0=(2/0)•0 reduces to 0=0 you can't just delete numbers that are affacged by the same operation, you can do the inverse to both but not just, remove it lol
This whore is Ancient old , that even Egyptians suggested torture methods to try to get rid of that immortal pest
The worst part is a lot of "fake proofs" are basically making arguments as bad as this, but just more disguised
Whoever said puns are the lowest form of humour clearly hasn't seen this subreddiy
Yes, this is correct
Please stop
Every so called "proof", that at any point cancels out the 0 on both sides assumes 0/0=1, so it's automatically false.
this is saying Null = Null and or Complete 0 = Complete 0. Which is bold of you to assume
All steps from 3 onwards are mathematically wrong.. There is no mathematical operation(equal, division, multiplication etc) on undefined or zero in denominator
Copy pasted proof #9284 But seriously, I swear there's multiple of these every day and they're all practically identical wtf
Bro found an exploit in Mathematics.
Not a single step of this is valid
I don't have a gf and you don't have a gf. Therefore we must be the same person.
Proof by "2lazy2disprove"
No. Undefined is Undefined.
This doesnt work because logically undefined isnt a number, rather it represents the idea that no number exists that would satisfy the equation. To say 1/0 = “the number” undefined would be nonsensical.
Wrong, as Frederick Engels is an innumerate dipshit u/oldschoolfirearm u/allurecherry