linear-algebra


Upper Division Linear Algebra


I am taking an upper division undergraduate linear algebra course, and I just need help understanding my reading, which states:
"Let S be a nonempty set and F be any field, and let F(S,F) denote the set of all functions from S to F. Two functions f and g in F(S,F) are called equal if f(s)=g(s) for each s, an element of S."
Basically, these 2 sentences make no sense to me, and I would greatly appreciate it if someone can break this down for me.
Thank you.
I think that in the sentence "equal if f(s)=g(s) for each s, an element of S." s mean all of the element S
so, In all case s, if f(s) and g(s) equal, function f=g

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