system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5 How do we know the fundamental rules of mathematics are true?

Who decided what would be the basic axioms/postulates of math (assuming of course they are axioms/postulates to begin with)?

  


I'm talking about rules like ".9999999999999999999999999999999 = 1" and "anything divided by 0" is undefined and "an nth root of a number is defined as this operation being done to it"

  


I know there must be some upper division math courses where this stuff is more thoroughly discussed, but would anyone care to give an ELI5 version?

  


**Edit:** the ".999999 = 1" question has been answered. Turns out, it's not so much a fundamental axiom as much as it is something determined by proofs. Thanks for the replies, please keep them coming,  they are very insightful!

  


**Edit 2:** Several people have already given their responses on the matter. However, if you have something to say, please add to the discussion! I read a lot of very helpful and concise replies way down at the bottom of the thread. I hope people get a chance to see those as well, and maybe add some more insightful thoughts/answers :-)
gpt
The basic rules of math aren't "true" as such. They have been _decided_. Math is not about "rules" it's about consequences.

Math is nothing but working on the mantra: "If these things are correct, then what?"

An interesting example of this is the Euclidean geometry that evolved into non-Euclidean geometry when some folks (Lobachevsky/Riemann/Bolyai) wanted to see what happened if the rules were slightly different. This, however, is beyond the scope of an ELI5, and readily available on the interwebz.