Allow me to offer a brief proof of the contrary.

You may select any real number between zero and infinity. We will call this R.

I will give you 1/R, which is between zero and one.

QED.

I believe you're conflating range, where it is trivially true that [0,∞] is of greater extent than (0,1), with quantity, where it is not the case that there exists a greater quantity of values in the former range than in the latter.