## Tonks 3 years ago More fun: 0 = 0 =0+0+0+0+0+... =(1-1)+(1-1)+(1-1)+(1-1)+... =1-1+1-1+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 = 1 Therefore 0 = 1, Q.E.D. Where's the problem?

1. Tonks

I don't need help, I just like to post fun things while I wait for other stuff. Can you find the problem in this reasoning? (there has to be a problem, or else all numbers equal each other and cease to have meaning!)

2. mathslover

there will be 1 at last?

3. mathslover

*-1

4. sauravshakya

I am not sure that can done or not because we dont know how many how many terms are there in 0+0+0+0+0... Infinity is unreachable.

5. sauravshakya

Sorry for typo

6. mathslover

yep u r right !!!

7. sauravshakya

Let there are n terms in 0+0+0+0+... Then Now, let 0=(1-1) Then (1-1)+(1-1)+... 1-1+1-1+1-1... Now this will have 2n terms........ and 2n will be even numbers. Now, 1-1+1-1+-1... =1-(1-1)-(1-1)+... If u will group that like that. and to get 1 there must be odd number of terms But we know it has 2n terms which is even. Thus, it cannot be 1

8. zugzwang

How about $0 = \sum_{0}^{\infty}0$is fine $0=\sum_{0}^{\infty}(1 - 1)$is fine But $0 = 1-1+1-1+1-1... = \sum_{0}^{\infty}(-1)^{n}$ is not fine ...?

9. henpen

$(1-1)+(1-1)+(1-1)+(1-1)+... \ne1 + (-1+1) + (-1+1) + (-1+1) +..$Evidently. But why? http://en.wikipedia.org/wiki/Grandi's_series http://en.wikipedia.org/wiki/Eilenberg%E2%80%93Mazur_swindle

10. UnkleRhaukus

error is from line four to line five a term is missing =1-1+1-1+1-1+1-1+... = 1+ -1 +1 + -1 +1 + -1 +1 + -1 ...

Find more explanations on OpenStudy