I was going through a Gaussian filter article and I suddenly came across this line In theory, the Gaussian distribution is non-zero everywhere. I gave it a couple of thoughts but couldn't satisfy myself. I would love to have others' opinions on it. Can someone explain to me in a simple term?

Thanks in advance.

CodePudding user response：

The probability of any number x in Gaussian Distribution is non-zero because of the way it's equation is designed.

f(x) will be very close to zero but still not zero for large x. Exp of a very large negative number is close to zero but not zero. In the graphs below, f(x) is asymptotic to x, not zero.