False mathematical proofs (idea) by waverider37

1=1²=(-1)²=√1, yes? Are we all familiar with that? (What? You're not? Oh, go take a math class.)
Therefore:
√1²=√(-1)²
=1 =-1 (since square roots always cancel out square powers)
Therefore 1=-1 and 2=0 (adding 1 to both sides).

So what's the problem? Well, the problem is: square roots do not cancel out square powers, although they certainly appear to. Ever heard of BODMAS or PEMDAS? Same thing, different acronym. Evaluate 1² or (-1)² first, then find the root of the answer. It ends up coming out to 1 both times.

Also: ever heard of the modulus or piecewise function? It's defined as √x² or |x|, and its graph looks like

          y
 \        |        /
  \       |       /
   \      |      /
    \     |     /
     \    |    /
      \   |   /
       \  |  /
        \ | /
         \|/
---------------------x
          |
          |

Note that y=x looks like:

         y
         |        /
         |       /
         |      /
         |     /
         |    /
         |   /
         |  /
         | /
         |/
---------------------x
        /|
       / |
      /  |
     /   |
    /    |

and nothing like our friend |x|.

God, I love proving stuff.

I can divide by zero	St. Petersburg Paradox	2^.5 = 2	The largest number that can be described in 14 words or less
Five is both even and odd	Pascal's f*cked-up theory of infinitude	Lies My Teacher Told Me	1=2
Stupid math tricks	Proof that all odd numbers are prime	The sum of an infinite series of positive numbers is negative	the smallest integer never considered
The prisoner's mistake	Proof that all triangles are isosceles	2+2=5	Chess Openings
Zero divided by zero	the disappearing area problem	1 = -1	There are as many numbers between 0 and 1 as there are in the set of all real numbers
imaginary number	Fermat's Last Theorem	Infinity is not a number