How can I read this mathematical sentence aloud in English? A map $s : \mathbb{N} \to X$ is a computable sequence in $(X,\nu_X)$ when there exists a computable map $f : \mathbb{N} \to \mathbb{N}$ such that $s(n) = \nu_X(f(n))$ for all $n \in \mathrm{dom}(\nu_X)$.
My best guess would be, "A map s taking N onto X is a computable sequence in the ??? (X, nu??) when there exists a computable map f taking N onto N such that s at n equals ??? of f ??? for all n elements of the domain of nu ???."
I am searching for a way to read it aloud that encodes all the elements of the sentence into speech.
 A: David Speyer wrote how I would say it in practise, in a context where I was writing it on a black/whiteboard. Here's how I would say it in a pub or walking down the street:
"Let's define a 'representation map for X' [or your own preferred jargon] to be just some partial function nu, from the natural numbers to X. Then we can define a computable sequence for that representation map nu to be any function s, from the natural numbers to X, which [is consistent with / agrees with / extends] the composition of nu with a computable function f on the natural numbers."
When using natural language, choose your nouns wisely and characterize them. Do you care about the ordered pair $(X,\nu_X)$, or really just the map $\nu_X$ (for which $X$ is just the background against which the idea is presented)? What is the role of the partial map $\nu_X$ in the idea you are communicating? Do you care about the integers $f(n) \in \mathop{\mathrm{dom}}(\nu_X)$ over which you quantify, or really just the domain of the composite function $\nu_X \circ f$? 
Identify the main characters in the synopsis of your play, and their roles: you will have a better chance of transporting the objects and morphisms of your idea faithfully to your interlocutors.
A: I would say "A map s is a computable sequence when there exists a computable map f satisfying certain properties" while writing down the property.
A: "A map ess from en to ex is a computable sequence in ex nu-ex when there exists a computable map eff from en to en such that ess of en equals nu-ex of eff of en for all en in the domain of nu-ex."
The hyphens are meant to indicate that the pause between these syllables is shorter than between two separated words.
Yes, I am not verbalizing that the X is subscripted, the ordered pair, or the difference between $n$ and $\mathbb{N}$. I assume you are talking about a situation where you are writing this statement on the board as you speak. Communicating any significant amount of math in a purely oral manner is incredibly hard because mathematical notation is much denser than ordinary spoken language; I find that I have to leave out some detail in order for the sentence to fit in my listener's head.
A: I would try to keep it really simple. Rather than verbalizing all the function and set symbols and subscripts, I would just say, "A computable sequence is the result of composing a notation after a computable function." I assume you're talking Computable Analysis theory and by $\nu_X$ you intend a notation $\nu_X:\subseteq \Sigma^* \to X$. Of course, this reading assumes your audience already knows what you mean by a notation and a computable function.
