1 plus 1 equals 2 why?

Answer 1

The explanation as to why 1+1=2 is complicated and I hope you understand it.

It's mysterious, 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. 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