## 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
 PhysOrg.com mathematics news on PhysOrg.com >> Pendulum swings back on 350-year-old mathematical mystery>> Bayesian statistics theorem holds its own - but use with caution>> Math technique de-clutters cancer-cell data, revealing tumor evolution, treatment leads
 Recognitions: Homework Help Science Advisor Oh dear, you didn`t happen to divide by zero did you?
 Recognitions: Homework Help Science Advisor 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.

Recognitions:
Gold Member
Staff Emeritus

## 1 = 2?? whats going on here??

Not only have "some" of us seen it before, it has been posted on this board more times that I want to remember!
 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.)
 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
 [sarcasm] this forum needs more post about how 1=0 and how .99999… doesn’t = 1 [/sarcasm]

 Quote by 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.)
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.
 There are a few other here: http://mathforum.org/dr.math/faq/faq.false.proof.html http://www.math.toronto.edu/mathnet/...econd1eq2.html I've seen one which involves integrals, but I can't find it...
 Recognitions: Gold Member Science Advisor 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.

Recognitions:
Homework Help
 Quote by Muzza There are a few other here: http://mathforum.org/dr.math/faq/faq.false.proof.html http://www.math.toronto.edu/mathnet/...econd1eq2.html I've seen one which involves integrals, but I can't find it...
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.
 there is a proof in the philosophy section about .999999999999999999999 = 1 using a geometric series

Recognitions:
Homework Help
 Quote by garytse86 there is a proof in the philosophy section about .999999999999999999999 = 1 using a geometric series
I assume you mean $0.99\overline{9}=1$ and there are many proofs of this.
 Interesting!, thanks for the links and integral 'proof'. I'll be sure to use that to confuse a few people ^^.

 Quote by Zurtex Try integrating $e^x \cosh x$ by parts: $$u = \cosh x$$ $$v' = e^x$$ $$\int e^x \cosh x dx = e^x \cosh x - \int e^x \sinh x dx$$
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.
 Recognitions: Gold Member i donno if it was posted here.. anyone can take on this: $$\int x^x dx$$

Recognitions:
Homework Help
 Quote by cronxeh i donno if it was posted here.. anyone can take on this: $$\int x^x dx$$