The Ministry of Silly Math

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

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s