# Math Help - Simple question on sets and bounds... dont laugh :p

1. ## Simple question on sets and bounds... dont laugh :p

On Upper and lower bounds - Wikipedia, the free encyclopedia
it says "2 and 5 are both lower bounds for the set { 5, 10, 34, 13934}"
how is 2 a lower bound when it is not even in the set?

3. A lower bound for a set $A\subset X$ is defined as number $x_0\in X$ with the property $x_0\leq a$ for all $a\in A$. It may be that $x_0$ in $A$, but it doesn't have to be. If $x_0\in A$ is a lower bound then it is automatically "the biggest lowerbound". Then $x_0$ is called a minimum of $A$.
If we look at your example, where we look at the given set as a subset $A\subset\mathbb{N}$. Then $x_0= 2, x_0= 5$ are both lower bounds. They satisfy $x_0\leq a$ for all $a\in A$. Even better $x_0 = 2$ is a minimum of $A$.