Proof that 1 equals 2

[daddy_4_eyes]

I came across this equation whilst reading a book. If 1 = 2, then 1 = any number...I am now afraid the world could explode because of this.

Anyway, all of the steps are perfectly legal except for one (good luck figuring out which one). You need to think back to high school algebra to follow this.

You may find the first step (a=b) the most confusing. But, this kind of thing is done all the time in Algebra. It's true for plenty of a's and b's. Assume that a is the number of ears on my head, and b is the number of ears on your head. In that case a=b.

a = b
multiply both sides by a
a^2 = a*b
subtract b^2 from both sides
a^2-b^2 = a*b-b^2
apply the distributive law to both sides
(a+b)(a-b) = b(a-b)
divide both sides by (a-b)
(a+b) = b
substitute all a's for b's (remember, if a = b you can do this)
a+a = a
regroup the two a's in the left side, and rename it 2a
2a = a
divide both sides by a
2 = 1

 

[gothecrows]

(a+b)(a-b) = b(a-b)
divide both sides by (a-b)

In case anyone is wondering - this is where the argument falls down:

a = b, so a-b = 0

You cannot divide by 0.

 

[daddy_4_eyes]

In case anyone is wondering - this is where the argument falls down:

a = b, so a-b = 0

You cannot divide by 0.

You know, you could of given it a bit of time before you destroyed that equation.
Now nobody will be amazed at this wonderful trick.

 

[Bryceson]

Wtf??!!

 

[crudbucket]

. Assume that a is the number of ears on my head, and b is the number of ears on your head. In that case a=b.

QUOTE]

My mate Chopper would like to have a quick word with you about this .....

 

[Mattlowry]

In case anyone is wondering - this is where the argument falls down:

a = b, so a-b = 0

You cannot divide by 0.

Uh this is a magic seven!

 

[mdc]

You know, you could of given it a bit of time before you destroyed that equation.
Now nobody will be amazed at this wonderful trick.

Anyone who's done maths at VCE level should either have seen this before or be able to spot the "trick" very quickly.

Anyone who hasn't probably won't care enough to be amazed

 

[Moonwatcher]

Was the book "Fermats' last theorem". I've previously killed threads by refering to this book.
Bigfooty users aren't excited about math. (much like my relationship with english)

 

[melbournemartin]

I've just come out of high school maths so that kind of stuff is easy to spot as the algebra is all so easy and recognisable. Feel free to post any more though as they are interesting

 

[BomberGal]

You know, you could of given it a bit of time before you destroyed that equation.
Now nobody will be amazed at this wonderful trick.

And nobody else got a chance to find the fault either...I guess I shouldn't have scrolled down first

 

[red+black]

You know, you could of given it a bit of time before you destroyed that equation.
Now nobody will be amazed at this wonderful trick.

Welcome to Year 8 maths. I think everyone has seen that.

 

[Sherrinator]

That was the lamest piece of crap ever.

How did any of that apply to anything a real human would give a shit about?

No offense intended.