Roy in Texas asked: On the number scale, an arrow head indicates infinity. Is there also infinity between 0 and 1. In other words if there is no largest number can there be a smallest number?
Thank you for the question, Roy. I have probably said on this blog that math has always been the bane of my existence. So, although I am confident a mathematician will have the real answer to your question, it will not be me.
That said, I will add that the answer is probably yes: there is an infinite number of partial numbers between "zero" and "one." I base that conclusion on the research being done by physicists who are continuing to look for matter that is smaller than quarks and leptons, which make up protons and neutrons, which make up atoms -- which, at one time, were thought to be the smallest particles of matter in the universe.
For all we know, there may be particles of matter even smaller than quarks and leptons -- so why not a number smaller than one but bigger than zero?