ELI5: Why 1+1=2

Because we define 2 to be "1+1".

In math, everything in made up. We invent the rules of reasoning that we can use to talk about math, we invent the rules that tell us how we can manipulate things and we invent the objects themselves. Math is like a board game, we invent the rules but once we play, we've committed ourselves to playing by the rules.

So, at some point, we have to invent 2. Starting out, we assume that we have something that we can call 0 and we assume that we have a process that will take in a number and output a new number that we call the "Next Number". We assign the picture "1" to "The Next Number After 0" and we assign the picture "2" to "The Next Number After 1". Instead of saying "The Next Number", we write "+1", just to keep things clean. So 1=0+1 and 2=0+1+1 which is 1+1.

If you heard that there's a book where they prove, after 300 pages, that 1+1=2, it took so long because they had to invent all the rules of math and invent all the objects in math and prove that everything worked how we thought it should work. Their goal was also not to prove 1+1=2, it was just kinda a joke they put in after they had enough work done to be able to prove it.

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