3 ms·
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
by judofyr 8y ago
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.
- RaitoBezarius 8y agoNot all linear functions possess a Taylor expansion, as not all linear functions are continuous, example: https://en.wikipedia.org/wiki/Discontinuous_linear_map https://en.wikipedia.org/wiki/Discontinuous_linear_map But, your statement is true for all real-valued linear functions AFAIK.
- ginnungagap 8y agoYou 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
- posterboy 8y agoThat 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.