i got such a set { |n is a natural numbers}
prove that inf { |n is a natural numbers}=0
n=1,2,3...
i know that the limit is 0 when n goes large
so the infimum is zero.
but i need to prove it by definition
i need to prove that 0 is the highest lower bound
suppose 0 is not infimum and there is t which t>0
and i need to desprove that t is the highest lower bound
?