Mathematics is often quoted as being one of the Universe's "absolutes." The following examples, which I have learned in my worldly travels, seem to prove the opposite.

Given: a, b = any real number not equal to zero

Given: b = a

ab = a²
[multiplied both sides by a]

ab - b² = a² - b²
[subtracted b² from both sides]

b(a - b) = (a + b)(a - b)
[factored]

b = a + b
[cancelled (a - b) from both sides]

b = 2b
[a = b is given]

1 = 2
[cancelled b from both sides]

[e-mail me if you want to know why this isn't true!]