The Internet features among its impressively large array of fantastically fun things a “proof” that uses basic algebra to demonstrate that 2 = 1:
a = b
a2 = ab
a2 – b2 = ab – b2
(a – b)(a + b) = b(a – b) (see Difference of two squares)
a + b = b
b + b = b (remember, a = b)
2b = b
2 = 1
The flaw, of course, is that since a = b, proceeding from the fourth equation to the fifth means dividing by zero. Don’t destroy the universe plzkthx.
I know a way to “prove” that 1 = 0 without resorting to such universe-shattering shenanigans. It begins with us considering this chunk of completely empty space:
Try to add all the numbers in this space, and you have the sum of no terms, AKA the empty sum, which is 0. Likewise, trying to multiply all the numbers results in the product of no factors, AKA the empty product, which is 1. With the reflexive axiom, we conclude that 1 = 0!
The flaw, of course, is that this proof relies on the reflexive axiom, which was previously disproven. |D