Question

why we use this theorem to prove (check) the limit of a function?
why we need a sequence ?
"limit f(x) = l as "x" approaches to "a" iff limit f(x_n) = l for every sequence x_n in the domain of f "

Answer 1

I think it's just a statement of continuum.
and it is a sequence because real line numbers is an "infinite sequence" of numbers the same meaning as it is continuous((but with that concept of infinite))