Map function to apply to each item of tuple Is there a mathematical function or notation for applying a function to each item of a tuple which returns a new tuple with items that correspond with the 'mapped' items of the original?
e.g. if $f(x) = x^2$ and $T = (1, 2, 3)$, it could be something like $map(T, f)$ which would return $(1, 4, 9)$.
 A: As your notation suggests, things like this are done in programming, often with a name like map. See the English Wikipedia page for the higher-order function "map" for discussion and notation. But in mathematical notation, this would not usually be thought of in quite this way. Depending on the emphasis/application, there are a few ways things might be phrased.
If the length of the input tuple is fixed and small, then we can use a (cartesian) product of functions: $f\times f\times f:\mathbb R^3\to \mathbb R^3$ would send $(1,2,3)$ to $(1,4,9)$. If it's fixed and large, I could imagine someone writing $f^{17}$ to denote $\underbrace{f\times f\times\cdots\times f}_{17\text{ }f\text{s}}$, but that would be so unusual it would need to be explained.
If the length of the tuple is not fixed (or infinite), then it would be common to use an ad-hoc notation for the sequences under consideration. Perhaps something like:

Let $(a_1,\ldots,a_n)$ be the finite sequence of [whatever]s. Then define $b_i=f(a_i)$ for each $i$, so that $(b_1,\ldots,b_n)$ has [whatever desired property].

If it's really necessary to be completely modular, then you'd have to define something brand new. Perhaps something like:

Taking inspiration from functional programming languages, if $\mathbf a$ is a finite sequence of reals $a_i$, and $f:\mathbb R\to\mathbb R$, we define $f_{>}(\mathbf a)$ [or $\mathrm{map}(f,\mathbf a)$, etc.] to be the sequence of corresponding $f(a_i)$.

