"Astounding: 1 + 2 + 3 + 4 + 5 + ... = -1/12"

[Dormie]

I assume some of you have seen this already...


Now I'm not a math wiz, but is this not inherently flawed in assuming that 1+1-1+1-1...=1/2? That is just a way for the measurer to make infinity finite in order to work with it, is it not? Thus ruining the whole problem.

[Kuntantee]

Infinity has some side effects on math.

Check this question http://math.stackexchange.com/questi...sy-zero-answer

[haxartus]

Infinity doesn't exist in real life.

[Deleted]

Infinity doesn't exist in real life.

Prove it. You can't. Infinity is used to quantify that which is currently not in a position to be observed but is incredibly likely to exist in the construct which the term infinity is being used in.

[Deleted]

its proven that 1-1+1-1+1.... and so on is 1/2, thats even talked about in the video and further explained in another numberphile thats linked.
so it all adds up to be correct.

i just LOVE that strange kind of things that happen with math. its just so mindboggling to tink about how math works in ways you would never have imagined. physics too btw.

thats why i love bradys channels

[Kraenen]

Prove it. You can't. Infinity is used to quantify that which is currently not in a position to be observed but is incredibly likely to exist in the construct which the term infinity is being used in.

wat. you can't prove infinity does exist

[Dormie]

wat. you can't prove infinity does exist

Start counting and tell me when you reach the end. Infinity as a number doesn't exist, but infinity as what it represents does.

its proven that 1-1+1-1+1.... and so on is 1/2

How can it possibly be proven? You can't decide to stop it, as the video says. And taking the average is not it either. It's just a way for them to know what doesn't really have an answer IMO.

[Kraenen]

its proven that 1-1+1-1+1.... and so on is 1/2, thats even talked about in the video and further explained in another numberphile thats linked.
so it all adds up to be correct.

i just LOVE that strange kind of things that happen with math. its just so mindboggling to tink about how math works in ways you would never have imagined. physics too btw.

thats why i love bradys channels

math does anything you want. it's all one big a priori tautology based on convention

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Start counting and tell me when you reach the end. Infinity as a number doesn't exist, but infinity as what it represents does.



How can it possibly be proven? You can't decide to stop it, as the video says. And taking the average is not it either. It's just a way for them to know what doesn't really have an answer.

no it doesn't. that's like saying God exists because the concept exists.

[Eviscero]

math does anything you want. it's all one big a priori tautology based on convention

And yet I challenge you to find another subject whose consequences equally well represent the observable.

[Dormie]

math does anything you want. it's all one big a priori tautology based on convention

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no it doesn't. that's like saying God exists because the concept exists.

That's not the same thing at all. There is no cap on the amount of things there can be, therefore the amount of possibilities is infinite. You can count for forever, that alone should be proof.

[Deleted]

sure it is.
but the rules are quiet simple, and what you can make with those simple rules is astounding.
sure, math itself is "madeup" by humans, but its aplicable everywhere around us. everything follows physics kind of which uses math.
thats the beauty of math. it can be used to describe basicly everything

[Biged781]

its proven that 1-1+1-1+1.... and so on is 1/2, thats even talked about in the video and further explained in another numberphile thats linked.
so it all adds up to be correct.

i just LOVE that strange kind of things that happen with math. its just so mindboggling to tink about how math works in ways you would never have imagined. physics too btw.

thats why i love bradys channels

No, it's not. This has already been debunked: http://blog.rongarret.info/2014/01/n...rs-is-not.html

Or, perhaps, an even more succinct explanation:

infinity + 7 = infinity

If you subtract infinity from both sides, you can tell the world 7 = 0!

As the article says, the rules which govern regular numbers do not apply to infinite sequences.

[Shadowsz]

There's a big fault with stating that the first set equals 1/2, there is NO axiom whatsoever that supports this decision.

Prove (and thus find) that axiom, and I'll believe it. Until that happens, this is a grand hoax.

Edit:

Because he based his calculations on something which is not, the end result becomes incorrect.

[Berianther]

You can't manipulate infinite series like that, so that's where the flaw is. In fact, you can "prove" that it is equal to any number you want by such manipulations.

[Hausdorff]

While there is a sense in which the series 1+2+3+... can be assigned a value of -1/12, it's not the normal sense of "if I add up this infinite list of numbers, I get -1/12".

It's more like "There's a function which is related to, but not equal to, the series 1+2+3+... that spits out a value of -1/12". The video really should have made that clear at the start.

In addition, some of the operations they perform on infinite series are just flat out not allowed. All in all, it's a poor showing from Numberphile.

[Deleted]

Okay so basically there is one thing that is not said in the video (at least I didn't hear it), it's that the equal sign here is badly used.

What is being done here is the zeta function regularization of the divergent sum of natural numbers which consists of assigning finite values to divergent sums of products (which are not finite values).

You can find more about it on Wikipedia (search "Zeta function regularization" on wikipedia, I'm not allowed to post links yet)

So to everyone thinking that the infinite sum of the natural numbers equals -1/2, you are in the wrong and this video is badly explained.

[Faldric]

I think this whole calculation crumbles when he takes the average of the alternating sequence. Because it will never be 0.5. At no point. Not even at the infinite point.
By setting the first sum = 1/2, they eliminated the alternating from all calculations on the Variable S.
But when they use the definitions of the sequences S1 and S2 they use the alternating values to cancel every second number out.

So they keep it on one side and cancel it on the other. No wonder some bull comes out of that.

[Eviscero]

Holy wow this is such a silly thing to do. Step 1 and they have already made a very strange choice. They define the infinite sum

S1 = 1-1+1-1+1 ... to be 1/2 because it is the AVERAGE of the two partial sums that can possibly be achieved: 0 and 1. Okay, fine... you're welcome to do that. I much prefer the standard approach which is to say an infinite sum is said to converge if the limit of the sequence of partial sums converges (that is define the sequence s(k) = the sum of the first k terms. If for every number epsilon > 0 there exists a natural number N such that |s(N) - L| < epsilon, we say the infinite sum "is equal" -- really converges -- to the number L). If no such L exists we say the sequence diverges (in other words is not equal to anything). There are some very interesting results about when an infinite sum converges and it should be pretty clear that S1 does not converge according to the definition proposed above. There are many reasons why the above definition "is the right one" and I am very curious to know in what context their averaging definition "is the right one."

[Kraenen]

That's not the same thing at all. There is no cap on the amount of things there can be, therefore the amount of possibilities is infinite. You can count for forever, that alone should be proof.

but that's my point, you can't prove that there is no cap on the amount of things there can be.

[Twoddle]

Reductio ad absurdum, or proof that the original assumption is false.