2 = 1?

[TheFlash1119 (OP)]

Try to find the mistake in the following set of equations which proves 2=1 using simple algebra:
Suppose you have two equal numbers (a and b). Then we can write:

a = b
(Multiply both sides by a)
a^2 = ab
(Subtract b^2 from both sides)
a^2 - b^2 = ab - b^2
(Factor both sides)
(a+b)*(a-b) = b*(a-b)
(Divide both sides by (a-b))
a+b = b
(Since a = b, substitute b in for a )
b+b = b
(Simplify)
2b = b
(Divide both sides by b)
2 = 1.

(BTW: a^2 is "a squared" or a*a)
I'm not sure if there's a way to hide text on the forums, but if there is, do that with your answer so everyone doesn't see. Enjoy

[Lividup64]

But it's not.

[Lividup64]

Also it seems very picky picky and conditional.

[Yvette]

Lit, now I can eat 2 servings of everything and still be on a diet

[luisc99]

I don't think there's a way to hide text on the forums. I could do it with CSS, but I can't really be bothered. And it's a bit iffy.

But basically, if a = b, then (a-b) = 0. You're dividing by (a-b) in step 4, which means you're dividing by 0. That doesn't work, so the proof doesn't work.

Similarly, by taking a factor of (a-b), you're basically multiplying both sides by 0. So your step 3, which is (a+b)*(a-b) = b*(a-b) basically reads (a+b)*0 = b*0, which is essentially proving 0 = 0. Even if the whole divide by zero thing didn't matter, the proof falls apart at this step too.

Nice try. You're not breaking maths on my watch

[Airbongo]

[OctoGamer]

Yall a bunch of fucking nerds

[_ForeverSwag878_]

Its not even valid.

Assuming b stays the same value throughout the problem,

2b cannot equal b


(omg i did math)

[Airbongo]

[OctoGamer]

[TheFlash1119 (OP)]

I don't think there's a way to hide text on the forums. I could do it with CSS, but I can't really be bothered. And it's a bit iffy.

But basically, if a = b, then (a-b) = 0. You're dividing by (a-b) in step 4, which means you're dividing by 0. That doesn't work, so the proof doesn't work.

Similarly, by taking a factor of (a-b), you're basically multiplying both sides by 0. So your step 3, which is (a+b)*(a-b) = b*(a-b) basically reads (a+b)*0 = b*0, which is essentially proving 0 = 0. Even if the whole divide by zero thing didn't matter, the proof falls apart at this step too.

Nice try. You're not breaking maths on my watch

CORRECT ANSWER!!! Congrats, Luis is the only (first) one here who solved it.

*DISCLAIMER: I AM GOING INTO NERD-MODE*
 Dividing by zero is probably the one mathematics rule people won't try to break/work around. In fact, if you allow dividing by zero, you can easily prove that 1 = 0 (just subtract 1 from 2 = 1), which can then be used to prove that z = 0 for all complex numbers z (Complex numbers are numbers of the form x + yi where i = the square root of -1). This can be expanded even further to make the claim that everything in this universe must equal zero, thereby proving that nothing at all exists in the material world. In other words, don't divide by zero.
*COMING OUT OF NERD-MODE*

Anyways, sorry to interrupt your normal everyday lives with some "nerd"-math and the possibility that everything you think you know doesn't even exist. Enjoy the rest of your day!