I have a question regarding the idea of a "constructible" function, in the sense that I can write down an expression for it.
For example, a bijection between $\mathbb{R}$ and its Hamel basis exists (under the Axiom of Choice), but its constructability in that sense is, in general, not attainable. We can prove its existence, but not necessarily write it in a closed form. Also, I am not necessarily interested in constructible function in a complex theory sense.
I personally think I am simply using a poor term for defining a function that can be expressed by some mathematical expression or relation, and I agree this could lead to some ambiguity (see constructive mathematics, e.g.). Nonetheless, I was wondering if there is defined nomenclature that I could use to better phrase what I am describing. Any references would be great!