[samatman]

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.

[grodriguez100]

> You may select any real number between zero and infinity.

Should that have been “between one and infinity”? Otherwise you cannot claim that 1/R is between zero and one.

[samatman]

You got me on that one.

I would prefer, given the domain, to amend to "given an R between 0 and infinity, I will return R for all R < 1, or 1/R otherwise". But yes, the proof was flawed.