Suppose that $\displaystyle x_n $ is a sequence of real numbers and $\displaystyle M \in R $
with $\displaystyle x_n \leq M , \forall n \in N $
if $\displaystyle x_n \to x$ for some $\displaystyle x \in R $
prove that $\displaystyle x \leq M$
Suppose that $\displaystyle x_n $ is a sequence of real numbers and $\displaystyle M \in R $
with $\displaystyle x_n \leq M , \forall n \in N $
if $\displaystyle x_n \to x$ for some $\displaystyle x \in R $
prove that $\displaystyle x \leq M$