Poll: Forget 0.999.... What's 1-1+1-1+1-1+...?

[Chaotic42]

As per the title, what's the sum of:

1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 +....

Enjoy.

 

[[DHT]Osiris]

I don't think you can add ellipses.

 

[sandorski]

Can not be Solved.

 

[Jaepheth]

It's what's known as a divergent sequence.
While it's bounded, it is not monotone (strictly increasing or decreasing)
EDIT: nor is it Cauchy (since you could have a convergent sequence that isn't monotone) Although proving it's bounded and cauchy would not necessarily prove it's convergent either.

https://proofwiki.org/wiki/Divergent_Sequences_may_be_Bounded



A better mind-f#ck is:
Consider the function F(x) = 1 when x is irrational and F(x) = 0 when x is rational (can be expressed as a fraction)
The function is nowhere continuous, and so is not Riemann integrable.
But the integral of F(x) from 0 to 1 = 1
(You can use something called Lebesgue integration combined with the fact that the measure of the rationals is 0[because the rationals are countably infinite])

 

[Chaotic42]

It's what's known as a divergent sequence.
While it's bounded, it is not monotone (strictly increasing or decreasing)

https://proofwiki.org/wiki/Divergent_Sequences_may_be_Bounded



A better mind-f#ck is:
Consider the function F(x) = 1 when x is irrational and F(x) = 0 when x is rational (can be expressed as a fraction)
The function is nowhere continuous, and so is not Riemann integrable.
But the integral of F(x) from 0 to 1 = 1
(You can use something called Lebesgue integration combined with the fact that the measure of the rationals is 0[because the rationals are countably infinite])

Baby steps, my friend. We don't want to scare them away.

 

[Jeeebus]

Given that all the 1s and -1s add up to 0, the answer is "...."

 

[A Casual Fitz]

There is no answer.

 

[master_shake_]

42.

i mean if it's not 7 or green the answer is always 42.

 

[SKORPI0]

Grandi's series

In mathematics, the infinite series 1 − 1 + 1 − 1 + ⋯ , also written

is sometimes called Grandi's series, after Italian mathematician, philosopher, and priest Guido Grandi, who gave a memorable treatment of the series in 1703.
It is a divergent series, meaning that it lacks a sum in the usual sense. On the other hand, its Cesàro sum is 1/2.

 

[jman19]

Cesaro or otherwise?

EDIT: Beaten to the punch

 

[IronWing]

Take the square root of the series FTW!