Does a 'converger' converge to a 'convergee'?

Question

I am trying to append suffixes to nouns 'related' (is there a more appropriate term?) by a verb. My example is from mathematics. Imagine a sequence S which converges to a limit L. Can I refer to S and L using terms derived from 'converge'? I thought of the words 'employer' and 'employee', and was led to these pages:

http://www.dictionary.com/browse/-ee
Which first says that '-ee' can be appended to an object of a transitive verb. But a quick search suggested that 'converges' in my example is an intransitive verb. So L can't be called a 'convergee'? The -ee link then says that

recent formations now also mark the performer of an act, with the base being an intransitive verb

If S is performing the act of converging, then does that mean that S can be called a 'convergee'?

http://www.dictionary.com/browse/-er
Suggests that the suffix '-er' can be appended to a verb to form an agent noun. If S is considered an agent, can S be called a 'converger'?

Now imagine that the sequence S is being studied for convergence to a limit L, but it may not converge. Can S be called something like a 'candidate converger/ convergee'?

Even if S does converge, it feels like a natural entity which happens to converge, and odd to think of as an agent. Does this (unsupported) argument make calling it a 'converger', even if acceptable, inappropriate?

I thought of the term 'integrand', but the origin seems to be a gerundive which I couldn't figure out how to use on a quick reading of its Wikipedia entry. Also, an integrand as the object of integration seems different from the convergence example.

Apologies if there are multiple questions bundled up in one. Also, I don't intend to introduce new terms, for the sake of it, to a well-studied behavior in mathematics! The exercise itself of adding suffixes to S and L might be badly-posed. Just curious.

Answer 1

I"m a mathematician, and I've never heard "converger" or "convergee". If I heard or read "converger", I'd understand what it's intended to mean, and I probably wouldn't object, since it's shorter than the standard term "convergent sequence". If I heard or read "convergee", I'd understand it, but I'd consider it rather silly, partly because "converge" is intransitive (it takes an indirect object, "converge to something", not a direct object), but mainly because we have a perfectly good, shorter, standard word for this, namely "limit".

A side comment about Lee Goldberger's answer: I advise caution in regard to "convergent" (as a noun) because it is often used to denote one of the terms of a sequence, not the sequence itself. This is especially the case in connection with continued fractions, where one speaks of, for example, the $n$-th convergent.

Answer 2

While not technically correct by pure definition in the context you present, the term 'converger' or 'convergent' are both correct to use in this case, assuming I have correctly followed your example.