So how is it that we can refer to them as the same thing? You reason that 0 cannot equal infinity because we cannot create an injective function from ∅ to ℕ. We could say 1=1, 2=2, 3=3 etc. or 0.5=1, 1=2, 1.5=3 etc. or .00001=1, .00002=2, .00003=3, etc. and we could keep going further and further down, but we could only ever come increasingly close to ∅ as we make new functions, because it is assumed that there can never be nothing. By the same token of reasoning, .9~ can infinitely approach 1, but it cannot be defined as the same thing. For it to work, we would have to put a limit on infinity. 0.0~1=1 (consider it the smallest 'conceivable' value without equaling ∅) to .9~=infinity, it could never equal 1, so 0.9~ =/= 1, because if there cannot ever be nothing, then there cannot ever be infinity.