Talk:Trigonometric functions: Difference between revisions

Revision as of 15:45, 14 February 2025

Revision as of 15:49, 14 February 2025

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:For example, in some fields of mathematics one can pick and choose among some axioms. Seemingly these axioms are not fundamentally true in all contexts, ready to be discovered, but merely are useful in some contexts. —[[User:Quantling|<span class="texhtml"><i>Q</i></span>uantling]]&nbsp;([[User talk:Quantling|talk]]&nbsp;&#124;&nbsp;[[Special:Contributions/Quantling|contribs]]) 15:22, 14 February 2025 (UTC)

::{{ec}} This is a part of a longstanding debate (see [[Mathematical platonism]]) on reality of mathematics. I agree that for trigonometric functions, the right term is "defined". For axioms the right terms are "stated" in the case of an axiom modeling the reality, such as the [[Parallel postulate]] or "chosen" in the case of the specification of the theory (there are many axiom systems that define the same theory. In the case of a theorem or a conjecture, I would use "stated". It is only for proofs that I would use "discovered". However, this does not cover the cases of wide theories and branches of mathematics, such as [[set theory]], [[infinitesimal calculus]], [[Probability]] and [[distribution (mathematics)|distribution theory]] for which I would use "introduced" or "initiated". [[User:D.Lazard|D.Lazard]] ([[User talk:D.Lazard|talk]]) 15:49, 14 February 2025 (UTC)

: I would also prefer "defined" or "introduced" in many cases. (I'm fine with "discovered" a theorem.) However, sometimes I have seen "invented", which I think is even worse than "discovered". [[User:Tito Omburo|Tito Omburo]] ([[User talk:Tito Omburo|talk]]) 15:24, 14 February 2025 (UTC)