Talk:Function of several real variables: Difference between revisions

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:Take any function {{mvar|f}} that has the real line or the complex plane as its ___domain. Knowing the ___domain of {{math|1/''f''}} amounts to know the zeros of {{mvar|f}}, which may be a difficult task. In the case where {{mvar|f}} is [[Riemann zeta function]], to specify the ___domain of {{math|1/''f''}} is equivalent with proving or disproving [[Riemann hypothesis]]. Not an easy task! [[User:D.Lazard|D.Lazard]] ([[User talk:D.Lazard|talk]]) 21:59, 23 November 2017 (UTC)
::In grade school, an ''extremely common'' [[abuse of language]] is to ask to "find the ___domain of" a given function, which indeed is putting the cart before the horse. What is really meant is "What is the maximal subset of <math>\mathbb{R}^n</math> on which we can use the given expression to define a function?", or even more succinctly, "On what subset of <math>\mathbb{R}^n</math> is this expression defined?". This is probably what is being meant by the statement in question.--[[User:Jasper Deng|Jasper Deng]] [[User talk:Jasper Deng|(talk)]] 22:05, 23 November 2017 (UTC)
: Thank both of you for helping to clarify this point. It seems to me that the expression {{math|1/{{var|f}}}} is not a function ''per se'', but might be if one specified its ___domain, codomain, and arguments correctly. Could someone who has a clearer picture of what this is trying to say rewrite it to actually be ''correct'' (i.e. not abuse language by talking about "functions", but rather "expressions")? Or maybe this is totally clear to most readers and I'm just pedantic :) [[User:Siddharthist|siddharthist]] ([[User talk:Siddharthist|talk]]) 05:47, 24 November 2017 (UTC)