Encyclopedia of Humor

It is proven that the celebration of birthdays is healthy. Statistics show that those people who celebrate the most birthdays become the oldest. — S. den Hartog, Ph D. Thesis Universtity of Groningen.

Theorem: 1 = -1
Proof:
1 = sqrt(1) = sqrt(-1 * -1) = sqrt(-1) * sqrt(-1) = 1^ = -1

Also one can disprove the axiom that things equal to the same thing are equal to each other.

1 = sqrt(1)
-1 = sqrt(1)
Therefore 1 = -1

As an alternative method for solving:

Theorem: 1 = -1
Proof:
x=1
x^2=x
x^2-1=x-1
(x+1)(x-1)=(x-1)
(x+1)=(x-1)/(x-1)
x+1=1
x=0
0=1
=> 0/0=1/1=1

Theorem: log(-1) = 0
Proof:
a. log[(-1)^2] = 2 * log(-1)

On the other hand:
b. log[(-1)^2] = log(1) = 0

Combining a) and b) gives:
2* log(-1) = 0
Divide both sides by 2:
log(-1) = 0

Theorem: 4 = 5
Proof:
-20 = -20
16 – 36 = 25 – 45
4^2 – 9*4 = 5^2 – 9*5
4^2 – 9*4 + 81/4 = 5^2 – 9*5 + 81/4
(4 – 9/2)^2 = (5 – 9/2)^2
4 – 9/2 = 5 – 9/2
4 = 5

Theorem: All numbers are equal.
Proof: Choose arbitrary a and b, and let t = a + b. Then

a + b = t
(a + b)(a – b) = t(a – b)
a^2 – b^2 = ta – tb
a^2 – ta = b^2 – tb
a^2 – ta + (t^2)/4 = b^2 – tb + (t^2)/4
(a – t/2)^2 = (b – t/2)^2
a – t/2 = b – t/2
a = b

So all numbers are the same, and math is pointless.