inf proof question..

its given that "x" is a low bound of non empty group A.
prove that x=inf A for e>0 there is "y" which x<=y<=x+e
??

i cant understand this question

i know how to prove that a certain number is inf or sup using only the formula of the group

but here i dont have the formula of the geoup
and i have this 'y' i dont know why its for??

i think i got it
A bounded from the bottom
x is a low bound of A

i need to prove that x=inf A


this expression is just the definition of inf
x<=y<=x+e


so i tried to solve it as if i got a formula
I presume that "x" is not inf
then our inf is x+e
now i proove that x+e is not infA
x+e>y

but here i got stuck because in this step i would do a formula operation.

??