# 1 = 2? whats going on here?

1. Jul 14, 2004

### ArmoSkater87

1 = 2?? whats going on here??

Haha, just wanted to show this, because its just so funny. I'm sure some of you have seen it before.

a = b
a^2 = b^2
a^2 - b^2 = ab - b^2
(a+b)(a-b) = b(a-b)
a+b=b
b+b=b
2b=b
2=1

2. Jul 14, 2004

### Galileo

Oh dear, you didn`t happen to divide by zero did you?

3. Jul 14, 2004

### Zurtex

If a = b then a - b = 0.

So this step:

(a+b)(a-b) = b(a-b)
a+b=b

Is not valid as you are dividing by zero. For example:

1*0 = 2*0

This does not prove 1 = 2.

4. Jul 14, 2004

### HallsofIvy

Not only have "some" of us seen it before, it has been posted on this board more times that I want to remember!

5. Jul 14, 2004

### Gza

The invalid step in this proof looks relatively obvious to me. I've seen some more intricate ones that aren't nearly as such, and take some time to figure out. (We've already had a few posts like this in the past, so I won't post them.)

6. Jul 14, 2004

### ArmoSkater87

hah, alrite, u guys saw it right away, it took me a little longer when i first saw it. I just though it would be fun to see some people's responses. :D

7. Jul 14, 2004

### JonF

[sarcasm] this forum needs more post about how 1=0 and how .99999… doesn’t = 1 [/sarcasm]

8. Jul 20, 2004

### KnowledgeIsPower

Just out of personal interest, could someone post or email me one of these more intricate and less noticable ones? I feel it would be an amusing email to confuse a few friends with.

9. Jul 20, 2004

### Muzza

Last edited: Jul 20, 2004
10. Jul 20, 2004

### Ivan Seeking

Staff Emeritus
Has anyone seen the, either 101, or 151, or 351 [?] page proof that 1 + 1 = 2?

I can't remember the page number for sure but the last page was posted in the office of a math professor of mine. I think it was done as a thesis to show that certain theories were consistent; like number theory and set theory, for example.

11. Jul 20, 2004

### Zurtex

Try integrating $e^x \cosh x$ by parts:

$$u = \cosh x$$
$$v' = e^x$$

$$\int e^x \cosh x dx = e^x \cosh x - \int e^x \sinh x dx$$

Using by parts method again on $e^x \sinh x$

$$s = \sinh x$$
$$t' = e^x$$

$$\int e^x \cosh x dx = e^x \cosh x - e^x \sinh x + \int e^x \cosh x dx$$

$$0 = e^x \cosh x - e^x \sinh x$$

$$\cosh x = \sinh x$$

And this reduces down to 1 = -1.

12. Jul 21, 2004

### garytse86

there is a proof in the philosophy section about .999999999999999999999 = 1 using a geometric series

13. Jul 22, 2004

### Zurtex

I assume you mean $0.99\overline{9}=1$ and there are many proofs of this.

14. Jul 22, 2004

### KnowledgeIsPower

Interesting!, thanks for the links and integral 'proof'. I'll be sure to use that to confuse a few people ^^.

15. Jul 30, 2004

### Dburghoff

Count up the negative signs: one from subtracting the result of the integration by parts, and one for using the derivative of $\cosh x$, which is $-\sinh x$. You should be adding the the antiderivative, not subtracting it.

16. Jul 30, 2004

### cronxeh

i donno if it was posted here.. anyone can take on this:

$$\int x^x dx$$

17. Jul 30, 2004

### Zurtex

Sorry I don't believe that is expressible in terms of elementary functions.