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I think x(3) would more commonly mean x times 3. f(3) would be function application. Even more context dependence.
by mkl 6y ago
I think x(3) would more commonly mean x times 3. f(3) would be function application. Even more context dependence.
- wcarey 6y agoRight. Of course, if you write x(3), other mathematicians should frown at you because you're making bad notational choices. It's a bit like explaining to students that the real way to know which 3rd declension nouns are i-stems in Latin is to say the genitive plural both ways. The one that doesn't sound wrong is correct. But you have to have a lot of time in the language for that to work.
- mkl 6y agoWell unnecessary parentheses are often used to indicate a substitution has happened. E.g. in a topic I just taught I would write things like ∫_{y=0}^3 x dy = [xy]_{y=0}^3 = x(3) - x(0) = 3x. In context I think it's perfectly clear and a good notational choice.
- wcarey 6y agoAnd so it is. edit: I suppose, what I'm trying to get at, perhaps too glibly, is that audience matters terribly much in mathematical writing. In the same way that Latin students don't start with Tacitus or Sallust, famous for their idiosyncratic grammar, math students shouldn't jump into the full context-dependent mess of the notation that experienced mathematicians use. But I think we often thrown them in unintentionally because we're so used to it.
- jacobush 6y agoYou used too little context when arguing with an audience who isn't used to that style of writing...
- C4stor 6y agoAlso, there are actual quite reasonable rules to know which 3rd declension nouns are i-stems, so it doesn't seem too right too just say "follow your gut". Btw, I wouldn't abuse latin comparisons on an american forum, I don't think it's quite in the culture ^^
- jerf 6y agox(3) is a function "x" being applied to the number 3, because "three times x" is 3x. Of course context would help resolve this if you have a function named x or not, or a variable named x or not, and if you have both a function and a variable named x, well, you worked for your confusion and you have obtained it; congratulations. :)
- jki275 6y agoI'm sure some would take it that way as "x" isn't commonly used in mathematical notation as a function name, the norm is to use f, g, etc. However, the notation is relatively clear notwithstanding. It almost has to be x as a function with an input of 3.
- wycy 6y agoI think x(3) would more commonly imply a function of 3, since you'd virtually always otherwise just write 3x.
- qubex 6y agoThis is one of the reasons I annoy people by following Wolfram’s convention in Mathematica of using square braces to denote arguments passed to a function: f(x)=fx=f×x while f[x] means “apply the function f to the argument x”. An unusual convention it may well be, but at least it’s one devoid of ambiguity.
- mkl 6y agoNot at all. f[x] is clearly the xth component of the array f :-D
- qubex 6y agoOn the blackboard in the mathematics department it’s not. But I get your point. I have also heard the objection that [x] is a 1×1 matrix whose only element is ‘x’.
- OscarCunningham 6y agoSquare brackets can also denote the floor function (especially in old works where '⌊' and '⌋' were typographically unavailable).
- gowld 6y agoAn array is merely a function from N to some set.
- pwdisswordfish2 6y agoIt's not devoid of ambiguity, because f[A] usually means the image of the set A under f.
- mkl 6y ago
- Wowfunhappy 6y agoIf you meant "function", would you generally write 𝑓(3) instead of f(3)? (I have no mathematics background past K-12)