proper way to denote a function f(n) vs f_n

Stream: new members

[rzeta0]

Which is the proper way to denote a function? The following compares $f(n)$ with $f_n$.

I'm not formally trained maths so I've been writing functions without thinking about it.

The reason I ask is because I've seen sequence elements denoted using the subscript format, eg $a_n$, so $f_n$ might be strictly seen as the $n^{th}$ element of the sequence generated by a function $f$. I don't really know.

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$$f_{n}=\begin{cases} \:0 & \;\text{if }n=0\\ \:2n-1+f_{n-1} & \;\text{otherwise} \end{cases}$$

or

$$f(n)=\begin{cases} \:0 & \;\text{if }n=0\\ \:2n-1+f(n-1) & \;\text{otherwise} \end{cases}$$

Aesthetically , I find the first form above easier on the eye.

[rzeta0]

I notice also the Lean aware editors allow subscripting too.

[Philippe Duchon]

There is no "right" way to do it. The $f_n$ subscript notation is traditionnally used for sequences, and the $f(n)$ parenthesized notation, for "functions"; but sequences are just functions from the naturals, so the distinction is arbitrary.