This is a bit strange. All the answerers have apparently misread the somewhat unusual question, and answered a more sensible variant instead. That more sensible variant would surely be a duplicate of something. The asker emphasized that the actual question is, indeed, about linear in/dependency in the space of functions with a singleton domain. Rendering all the answers wrong.

An unusual situation for sure, but the answers do not have any content worth preserving IMHO.

Needing more eyes here. Originally I, unwittingly, voted to close it as off-topic instead of using one the three dupehammers. Namely, the main part of the question was handled here a few weeks earlier. I wanted to use a close-reason other than dupe to avoid whining about the multiple parts etc. The question was closed soon enough, but some others reopened it, probably due to the edit.

But it is still a dupe, and now the system won't let me use my dupehammer!

Not urgent, obviously. And may be I'm out of line.

@JyrkiLahtonen I also find something odd about the edit history... what is with the addition of nonbreaking spaces around all of the mathy bits?

@JyrkiLahtonen I also think that this comment may indicate that the asker is very confused about what it is that they are asking.