1. ## sequence 2

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

2. Originally Posted by flower3
Suppose that $x_n$ is a sequence of real numbers and $M \in R$
with $x_n \leq M , \forall n \in N$
if $x_n \to x$ for some $x \in R$
prove that $x \leq M$
Suppose that $x>M$.
So in the definition of converence use $\varepsilon = {x - M} > 0$.

3. Originally Posted by flower3
Suppose that $x_n$ is a sequence of real numbers and $M \in R$
with $x_n \leq M , \forall n \in N$
if $x_n \to x$ for some $x \in R$
prove that $x \leq M$
You're welcome for the help in your other thread, by the way.