MJ: Mathematical Proof: 2=1 (Non-bj)

[MJ]

Hey guys,

I came across this "proof" on the net and figured some of you might be interested so here goes:

Proof: 2 = 1

Given a = b,
a^2 = ab
a^2 - b^2 = ab-b^2
(a-b)(a+b) = b(a-b)
a+b = b
b+b = b
2b = b
2 = 1 ???

Any takers?

MJ

[DanM]

> Hey guys,

> I came across this "proof" on the net and
> figured some of you might be interested so here goes:

> Proof: 2 = 1

> Given a = b,
> a^2 = ab
> a^2 - b^2 = ab-b^2
> (a-b)(a+b) = b(a-b)
> a+b = b
> b+b = b
> 2b = b
> 2 = 1 ???

> Any takers?

> MJ
You divided by zero when you divided both sides by a-b

[Norm Wattenberger]

[Don Schlesinger]

> Hey guys,

> I came across this "proof" on the net and
> figured some of you might be interested so here goes:

> Proof: 2 = 1

> Given a = b,
> a^2 = ab
> a^2 - b^2 = ab-b^2
> (a-b)(a+b) = b(a-b)
> a+b = b
> b+b = b
> 2b = b
> 2 = 1 ???

> Any takers?

Specifically, on these two lines
(a-b)(a+b) = b(a-b)
a+b = b,
you are presumably dividing both sides by a - b. But, since a = b, a - b = 0, which isn't permitted.

"Proofs" like these demonstrate why division by zero isn't allowed. It would lead to all sorts of internal inconsistencies and silly outcomes, such as the one above.

Don

[MJ]