lets-f-R-R-and-g-Z-R-such-that-f-x-g-x-x-Z-given-a-Z-then-proof-or-give-a-counter-example-that-lim-x-a-f-x-g-a-

Question Number 1192 by 123456 last updated on 13/Jul/15

lets f : R \to R and g : Z \to R such that

f (x) = g (x), x \in Z

given a \in Z, then proof or give a counter example that

\lim_{x \to a} f (x) = g (a)

Commented by prakash jain last updated on 13/Jul/15

Limit may not even exist for f (x) .

Answered by prakash jain last updated on 14/Jul/15

g (x {= x

f (x) = {\begin{cases} x & x \in Z \\ 0 & x \notin Z \end{cases}