General

@metaghost4:

let k = 1 - 1 + 1 - 1 + 1 ...
k = k
1 - 1 + 1 - 1 + 1 ... = 1 - 1 + 1 - 1 + 1 ...
1 + (- 1 + 1) + (- 1 + 1) ... = (1 - 1) + (1 - 1) + ...
1 + 0 + 0 ... = 0 + 0 + ...
1 = 0
so k = 1 and k = 0

either i have a functional programming language, or k = 1. this statement must be true, since k = 1 is true, and any statement OR-ed with a true statement is true. so is the statement 'either i have a working program or k = 1', since it's exactly the same statement. but let k = 0, which is true.
if that's the case, then k = 1 is false, which means i have a working program. q.e.d

@ulti25: I. Love. You.

[quote=GoldenBow]I can't remember whee but someone posted how every answer can lead to a certain number like 4 or something. I'd love to find it again.[/quote]

Pick a number and count the number of letters that number has. For example, six has three letters.
Now, go to that number and count the number of letters it has. Three has five letters.

Continue doing this and you'll always end up at four, which isn't a surprise since four is the only number that has the same number of letters as the quantity it represents. All other numbers lead to another number while four will just reference itself.

Post this on math.stackexchange.com and see what they have to say.

[quote=ehnogi]@razormana: Infinite divergent series don't converge. That's the point. There is no definitive value when you're saying that something is infinitely adding up. It is a singularity. I just found this to be interesting and it blew my mind.

@PurpleWaffle: Yeah. You're right. Who wants to write Euler's method?[/quote]

The point is you are assuming there is an average and that it is 0.5. You also neglect to take a negative infinity when you shift to S2.
That proof is filled with flaws, physics can accept it as a proof, maths cant.

I can't remember whee but someone posted how every answer can lead to a certain number like 4 or something. I'd love to find it again.

It's -1/12 you peasants need to learn to math

@metaghost4: i already made it, and i can prove it works ^^

Well wait if you just keep adding numbers forever then no crap, Sherlock - of course it's infinity.

baby's first proofs course?
I shouldn't make jokes I'll probably fail it next semester

@razormana: Infinite divergent series don't converge. That's the point. There is no definitive value when you're saying that something is infinitely adding up. It is a singularity. I just found this to be interesting and it blew my mind.

@PurpleWaffle: Yeah. You're right. Who wants to write Euler's method?

1 + 2 + 3... doesn't actually equal -1/12, -1/12 is the value assigned to this particular series through a summation method.

It's not very safe to manipulate divergent series as if they were finite sums. You can get led to inconsistent results. I'm aware (although I don't know enough to speak much about it) of things like zeta function regularization to get around divergent series, and iirc it can lead to results that are consistent with expected phenomenon in quantum mechanics, but this doesn't mean that the series actually sums to that number itself as far as I'm aware of.

I may be off as this isn't a topic I've covered in much depth (and I imagine most on this forum haven't) but this is what I've gathered. It's probably sort of like how Euler's formula seems mystical and magical if you only see the derivation of the relationship between the exponential and trigonometric function through Taylor series, but once you learn more about the complex plane it becomes a little more obvious.

I don't follow.

The infinite series for A is actually divergent because the partial sum is always either 1 or 0, so the "average" A=1/2 is not even a viable answer.

When doubling a series, you aren't allowed to "shift the series over" and then adding, because then it will be adding two different series. 2B is actually [2-4+6-8+10-12+...].
Therefore, 2B =/= A and B =/= 1/4.

For C-B, you aren't allowed to take out the zeros and call it C again. It needs to be given a new name "D".

Using a letter to name a series okay as long as the sigma notation is defined with it. Otherwise, you'll get in some trouble with applying algebraic concepts to infinite series.

[quote=metaghost4]Then why don't you make this into a functional programming language?[/quote]

Because he is using fundamentally flawed maths. As several people on the video @polymerase linked (probably where op got it from)
You could just as easily say it equals any other number and by that maths it is still correct.
This infinite sum doesn't work, because we cant define infinity as 0 or 1 (even or odd) he is taking the "average" or "intermediate" which is just crap that mathematicians use to try to prove something that in all sense of the word is undefined, its the same as dividing by zero its undefined.
Inb4 the same youtube channel proves you can divide by zero in a similar fashion.

http://www.youtube.com/watch?v=w-I6XTVZXww

with that logic, you can literally prove anything

@nopaycheck:

But that proof though.

That shows that math is a flawed language, not a law.