inf proof question..

[transgalactic]

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??

 

[transgalactic]

i know that inf is the biggest integer under the lower bound
and if we add a certain "e" then it will cease to be inf
and it will become inside the group