Post #4355848
2026-08-02 23:52 UTC
@bemmesr@mathstodon.xyz
"so I'll at least give you that there are not *many* textbooks published in the last 150 years which differ on the order of operations" - there aren't ANY which differ on the order of operations
"of course we have no reason to believe this to be the case" - we have EVERY reason to believe it's the case - proofs 🙄
"arithmetic is essentially just an axiomatic system" - nope. Literally proven, but feel free to try and find an example of 1+1=3. I'll wait
Replies (1)
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@bemmesr@mathstodon.xyz 2026-08-03 11:47
@SmartmanApps@dotnet.social you say that arithmetic is ‘literally proven’, which I do agree with to some extent. For example, the Principia Mathematica by Whitehead and Russell proves much of the foundations of modern mathematics, but it does use some axioms to begin with. That is, it doesn't just prove these things out of nowhere, but builds up each proposition from some basic *assumed* facts. My question then is, are you suggesting that you can prove mathematical truths without any axioms? If so, could you provide an example of such a proof?