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What are some good alternatives to avoid mix-up with $f(x)$ where f is a function and $f(x)$ where f is a constant? I was thinking of some additional symbols to the f-symbol, $f_{x}(x)$, or maybe using different brackets $f[x]$, but I'm mostly hoping that there were already some professionally used alternatives to imitate.

Thanks in advance

Frank Vel
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  • Writing $4(5) = 20$ is only one way to write product, and how you do it pretty much comes down to what country you're from. Other common options include $4\cdot 5 = 20$, $4 \times 5 = 20$ and $4.5 = 20$. There are many options. Also, you always declare what your letters mean, so it should be clear from the context whether $f$ is a function or a constant. There is another option as well: include the variable in the function name, i.e. write $f(x)(a+b) = f(x)a + f(x)b$. Not neat, but removes some ambiguity. One also usually, in a product, write the functions last and scalar coefficients first. – Arthur Sep 17 '14 at 14:22
  • It's a matter of convention. $f$ is not usually used as a variable. If you must, you can try to remove ambiguity by writing for instance: $f\times(a+b)$. – Martigan Sep 17 '14 at 14:23
  • FWIW, in set theory $f[x]$ is already taken as it is often used to distinguish between the image $f(x)$ of an element $x$ of the domain of $f$ and the image $f[x]$ of a subset $x$ of the domain. In everyday mathematics, you will rarely if ever have the chance to confuse the two, though. – Frunobulax Sep 17 '14 at 14:30

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I know how you feel; I used to worry about this all of the time. The key thing to remember, however, is that the meaning should be clear from context.

I believe Mathematica uses brackets for functions, though, if you're set on changing notations.

Robin Goodfellow
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  • I fully agree. Mathematical notation is meant to convey information to other human beings, so it is OK if it's a bit ambiguous as long as the intended readers will be able to figure out easily what you meant. If you're "talking" to a machine (as in: Mathematica), that's another story. – Frunobulax Sep 17 '14 at 14:33
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Normally scalars get put before vectors and functions to avoid this ambiguity - I would always assume $(a+b)f$ to be $af + bf$ and $f(a+b)$ to be $f$ evaluated at $a+b$.

If you're worried you could use $f[x]$, or always put $(a+b) \cdot f$ or something. I think the best thing really is to just follow the known conventions and be consistent (so if something is ambiguous, the reader has a context to put it into and figure it out).

Matt Rigby
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The standard notation for continuous linear functional is $$\langle f, x\rangle_{X'\times X}$$

I guess we can do something like $$\langle f, x\rangle_{C(\mathbb{\mathbb{R}}) \times \mathbb{R}}$$ for continuous functions.

Xiao
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  • That notation for continuous linear functionals is designed to be consistent with the use of $\langle \cdot , \cdot \rangle$ for inner products in Hilbert spaces where the dual is just itself. I would always assume notation using $\langle$ and $\rangle$ to mean something linear and would find that second notation ambiguous. – Matt Rigby Sep 17 '14 at 14:39
  • yeah, good point about the linearity. – Xiao Sep 17 '14 at 14:44