User blog comment:B1mb0w/Alpha Function/@comment-1605058-20150627140104/@comment-1605058-20150627182312

From your explanation I can see that it's not always true that if \(a<b\) then \(\alpha(a)<\alpha(b)\) - e.g. if you take \(a=0,b=0.5\). Of course, this is unavoidable if you want to have all integer outputs, I just wanted to point that out.