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

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.

• If you are interested in the particular word converge, I suggest you try an example outside of mathematics. (Traffic, maybe?) Mathematics has a very well defined set of terms and no one would consider "switching it up" in this case. May 9, 2017 at 6:33
• Feeders feed into a trunk in automotive and network traffic.
– Davo
May 9, 2017 at 11:42
• Possible duplicate of "-ee" and "-er" word endings May 10, 2017 at 12:17