this post was submitted on 12 Jun 2025
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To be fair, the first 100 pages of that was justifying the set theory definition for what numbers are. The following two hundred papers are proving that a process of iterative counting we call addition functions in a consistent and useful way, given the set theory way of defining numbers. Once we get to that point, 1+1 is easy. Then we get to start talking more deeply about iteration as a process, leading to considering iterating addition (aka multiplication), iterating multiplication (aka exponents), etc. But that stuff is for the next thousand pages.
Remember, 0 is defined as the amount of things in the empty set {}. 1 is defined as the amount of things in a set containing the empty set {{}}. Each following natural number is defined as the amount of things in a set containing each of the previous nonnegative integers. So for example 2 is the amount of things in a set containing the empty set and a set containing the empty set {{}, {{}}}, 3 is the amount of things in a set containing the empty set, a set containing the empty set, and a set containing the empty set and a set containing the empty set {{}, {{}}, {{}, {{}}}}, etc. All natural numbers are just counting increasingly recursively labeled nothing. Welcome to math.