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

?