Thread: infimum of set proof

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

?

Originally Posted by transgalactic

i got such a set { |n is a natural numbers}
prove that inf { |n is a natural numbers}=0
n=1,2,3...

You know that 0 is a lower bound for that set.
If show that there is some is the set such that .

i dont know how to show that there is a number in the set which is smaller then c

?

Originally Posted by transgalactic

i dont know how to show that there is a number in the set which is smaller then c

If there is a positive integer
such that so .

thanks i got it