Oops I broke the laws of math.

[stargroup]

When someone fixes the proof I'll post another one in which I break the laws again.

P.S. If you think this is too easy for you don't ruin it for others. Let them figure it out.


Proof 1: 3=2

-6 = -6

9 - 15 = 4 - 10

9 + (25/4) - 15 = 4 + (25/4) - 10

(3 - 5/2)(3 - 5/2) = (2 - 5/2)(2 - 5/2)

(3 - 5/2)² = (2 - 5/2)²

3 - 5/2 = 2 - 5/2


3 = 2


Proof 2: 2=1

a = b

a² = ab

a² - b² = ab - b²

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

a + b = b

2b = b


2 = 1


Proof 3: 1=-1

-1 = -1

1/-1 = -1/1

√(1/-1) = √(-1/1)

√1 / √-1 = √-1 / √1

√1 * √1 = √-1 * √-1

√1 = √-1


1 = -1


Alternate version of Proof 3:

1 = √1 = √(-1)(-1) = √-1 * √-1 = -1


Proof 4: 0=1

0 = 0 + 0 + 0 + 0 + ...

0 = (1 - 1) + (1 - 1) + (1 - 1) + (1 - 1) + ...

0 = 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + ...

0 = 1 + 0 + 0 + 0 + ...


0 = 1


Proof 5: 1=0

x = 1

(d/dx) x = (d/dx) 1


1 = 0


Proof 6: 2=1

x² = x * x = x + x + x + x ... (x times)

(d/dx) x² = (d/dx) x + x + x + x ... (x times)

2x = 1 + 1 + 1 + 1 ... (x times)

2x = x


2 = 1


Proof 7: Sum of all positive integers is negative.

S = 1 + 2 + 3 + 4 + 5 + 6 + 7 + ...

A = 1 - 2 + 3 - 4 + 5 - 6 + 7 - ...

S-A = (1-1) + (2-(-2)) + (3-3) + (4-(-4)) + ...
= 4 + 8 + 12 + 16 + ...
= 4S

S+A = (1+1) + (2+(-2)) + (3+3) + (4+(-4)) + ...
= 2 + 6 + 10 + 14 + ...
= 2 + (4+2) + (8+2) + (12+2) + ...
= 4S + (2+2+2+2+...)

(S-A) + (S+A) = 2S = 8S + (2+2+2+2+...)

-6S = (2+2+2+2+...)


S = (-1/6)(2+2+2+2+...)



Mind blown yet?