Is 2 Really Equal to 1? A Mathematical Paradox

[Himal kharel]

let a=b
a²=ab
a²-b²=ab-b²
(a+b)(a-b)=b(a-b)
a+b=b
a+a=a<from above>
2a=a
2=1
PROVED

 

[Doc Al]

When you divide by zero you can 'prove' all sorts of nonsense.

 

[arildno]

Here's another classic, using "i" as the square root of (-1).
Can you spot the error?

1=\sqrt{1}=\sqrt{((-1)*(-1))}=\sqrt{(-1)}*\sqrt{(-1)}=i*i=-1
That is:
1=-1

 

[BloodyFrozen]

let a=b
a²=ab
a²-b²=ab-b²
(a+b)(a-b)=b(a-b)
a+b=b
a+a=a<from above>
2a=a
2=1
PROVED

The part in red

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

Remember we defined a=b, therefore (a-b) must equal zero. You can't divide zero as it is a division error.

 

[micromass]

Check http://mathfail.com/2010/11/where-is-your-god-now---meme-math-style.html for more goodies!