Two is one

[Brom]

a = b
aa = ab
a^2 = ab
a^2 - b^2 = ab - b^2
(a+b)(a-b) = b(a-b)
a+b = b
b+b = b ...(since a = b)
2b = b
2 = 1

What's wrong here?

[Borodog]

You divided by zero.

[soon2bepro]

you multiplied by zero. just because 2*0 = 0 and 1*0= 0 doesn't mean 2 = 1

[Brom]

Thanks guys, I knew I was missing something simple.

[ihardlyknowher]

I don't see how:

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

Also, if a+b=b, then a by definition is zero. Thus, b=0 and you just typed:

0=0
0=0
0=0
0=0
0=0
0=0
0=0
0=0
2=1

[soon2bepro]

say a = 1

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

(1+1)(1-1) = 1(1-1)
2*0 = 1*0
0 = 0


the problem here, is that ANYTHING * a-a = 0.