What Does It Mean for a Function to Have Compact Support?

[mnb96]

Hello,
given a function f:R->R, can anyone explain what is meant when we say that "f has compact support"?

Some sources seem to suggest that it means that f is non-zero only on a closed subset of R.
Other sources say that f vanishes at infinity. This definition seem to contradict the previous: for example the Gaussian is never 0 but does vanish at infinity.

So, where is the misunderstanding?

 

[mathman]

Compact support means the function is zero everywhere outside some finite interval. Gaussian does not have compact support.

 

[disregardthat]

It naturally means that the support of the function is a compact set, or equivalently as mathman points out; contained in a finite closed interval. This implies that f must vanish at positive and negative infinity, but is not equivalent as your example shows.