Comment by practal
25 days ago
Just to make clear, so you are saying Serge Lang is wrong, too? And as proof you cite various anonymous HN users, most of them heavily downvoted?
> I agree it's inaccurate to say it's decided primarily by Foundations vs Analysis, but I'm not sure how else to slice the pie.
Seems you agree with me after all.
> I agree it's quibbling, but it's harder to teach maths to people if these False Friends exist but don't get pointed out.
A distribution is a function, but considered on a different space.
It is even harder to teach math to people by insisting that above fact is wrong. Schwartz got a Fields medal for this insight.
It’s strange to hear a fellow mathematician say that if I’m in set theory class then a functional is a function but isn’t one in functional analysis. In Rudin’s Functional Analysis book he proves that linear mappings between topological spaces are continuous if they are continuous at 0. I’ve never heard of someone believing that a continuous mapping is not a function.
Terry Tao writes in his analysis book:
Functions are also referred to as maps or transformations, depending on the context.
Tao certainly knows more about this than I ever will.
Yeah, the whole argument felt somewhat unhinged and silly. It is fine to point out that sometimes "function" is used in a more specific manner than "mapping", particularly in analysis, but I doubt any mathematician would think that a functional is not a function, in a general context such as a HN comment.