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.