Does a function with no zeros (i.e. $f(x) = c \ne 0$) have a finite number of zeros?

Question

I am dealing with a set of functions with finitely many zeros. Are functions without any zeros included in that set, for example $f(x) = c \ne 0$?

Answer 1

Yes, as the empty set is finite.

Edit: A common definition of a set $A$ to be finite is that there exists a injection $A\to\mathbb{N}$ but no surjection $A\to\mathbb{N}$. The empty set certainly satisfies this, so it is finite.

Answer 2

They certainly are.

Let $f $ be a function with no zeroes. Let $A $ be the set of all $x$ such that $f(x)=0$. $A = \emptyset $, thus the cardinality of $A $ is $0$. $0$ is a finite number so $f $ is in your set.