How do you prove that one plus one equals two? - Answers

Because if you have one apple and then take another and put it with that one apple you would then have two apples. Therefore 1 + 1 = 2 ANSWER 2- Well you could test it by going 2 - 1 = 1, but somethings in math you just have to go along with, it just works ANSWER NUMBER 3: Russell's & Whitehead's proof uses pure symbolic logic. It's pretty arcane, though, because first you have to come to a definition of what "1" means, what "2" means, and even what "+" & "=" means! It's a lot harder than you think without using circular definitions (eg "1" is when there is only one of something - this won't do as a definition). The proof goes something like this (remember, it depends on set theory): We start off by defining the natural numbers (ie positive integers) in terms of sets. For any set S, define a "successor" function f as f(S) = {S, {S}} ie, the set containing: S and the set containing S. Then we define the natural integers as such: Define the number 0 to be the empty set, which I'll write here as O. Then each successive integer (ie "n+1") is just the preceding integer put through the successor function, ie 1 = {O, {O}} 2 = {O, {O, {O 3 = {O, {O, {O, {O} and so on. Then 1+1=f(1)={O, {O, {O=2. QED. By the way, from this definition of natural integers we can work out the entire system of arithmetic, including rational numbers, irrational & transcendental numbers, multiplication, division etc...