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