[getting back to work on the first weekday after a new year] okay so what is an integer again
@vogon In fairness, mathematicians have struggled quite a bit with that question.
@neal @vogon “The integers are the only nontrivial totally ordered abelian group whose positive elements are well-ordered.”
“This is equivalent to the statement that any Noetherian valuation ring is either a field—or a discrete valuation ring. ”
That's cleared that up then.
@ersatzmaus @vogon Some of these terms are barely a century old and for better or worse, pretty much none of them have percolated into primary or even secondary education.
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@neal @vogon “The integers are the only nontrivial totally ordered abelian group whose positive elements are well-ordered.”
“This is equivalent to the statement that any Noetherian valuation ring is either a field—or a discrete valuation ring. ”
That's cleared that up then.