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Comment by jackpirate | Hacker News Reader

A function with a linear type uses it's parameters exactly once. The concept of "linear type" doesn't relate to a the concept of "linear function" except in an abstract mathematical way.

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Well, a linear function is a function where you can only use the parameter once when expressed in its Taylor expansion. E.g. these are not linear: x^2=x*x (used twice), exp(x)=1+x+... (used infinite times). It’s a very symbolic way of thinking about it though, and not what you usually consider an important property of linearity.

Not all linear functions possess a Taylor expansion, as not all linear functions are continuous, example: https://en.wikipedia.org/wiki/Discontinuous_linear_map

But, your statement is true for all real-valued linear functions AFAIK.

You still need to worry about the domain, in general there are plenty of real valued discontinuous linear functions (or functionals) from an infinite dimensional Banach space to R.

In finite dimension however linear functions are continuous

That is a badly written article. And the ones for linear map and continuity linked there, which would be important to the topic, too. The good mathematical articles start with a definition after the intro.

So much for teaching year olds. This is not rocket science, but mathematicians (almost inherent) inability to have language skills makes it seem so, notably.

This makes sense, but I don't see how it explains the difficulty the kid was having.

6+a*x, a->0

same but different:

6+x/a, a->infinity

imho constant is a special case of linear

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