this post was submitted on 20 Oct 2024
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This guy would not be happy to learn about the 1+1=2 proof
Isn't "1+1" the definition of 2?
That assumes that 1 and 1 are the same thing. That they’re units which can be added/aggregated. And when they are that they always equal a singular value. And that value is 2.
It’s obvious but the proof isn’t about stating the obvious. It’s about making clear what are concrete rules in the symbolism/language of math I believe.
Isn't 1 and +1 well defined by the Peano Axioms by using the intersection of all infinite successor functions and starting at the empty set?
It depends on what you mean by well defined. At a fundamental level, we need to agree on basic definitions in order to communicate. Principia Mathematica aimed to set a formal logical foundation for all of mathematics, so it needed to be as rigid and unambiguous as possible. The proof that 1+1=2 is just slightly more verbose when using their language.