Letters To Aletheia

A Simple Proof That 1 + 1 = 2

Let us define point O. 

Let us extend line OX from point O that is any arbitrary length, denoted x. 

Let us extend line OX by length x forming line OXY. 

The combined length of OXY is 2x represented by the equation 1x +1x = 2x.

We can divide both sides of this equation by x.


1 + 1 = 2


Let this combination of values in the same dimension be termed addition (as denoted by ‘+’ in the equations above).


Discussion: I couldn’t find a clear proof of 1 + 1 = 2 anywhere on the internet so the above serves to illustrate exactly what I mean when I say 1 + 1 = 2. In plain English it is my view that numbers are a tool to analyse a single dimension denoted by the units attached to the number where applicable be that spacial, temporal or abstract.