09 April 2006

Infinity Plus One

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?

1 comment:

Roy said...

Well, darn. I had hoped with the Universes bumping up against each other post that my question mught spark at least a short string. I guess that shot that theory. (pun intended)

The math is that every number between 0 and 1 can be expressed as 1/n where n is any number. If n = infinity then the numbers between 0 and 1 is 1/infinity.

But the math is not what I was going for. If there is no smallest number there is no smallest particle.

If I were the "incredible shrinking man" and lived forever, I would shrink forever and any solid object I landed upon, I would eventually fall through.

So if you put me on your hand (at a poitn where I was small enough to do that, and I shrank a the proper rate I could fall forever and never fall out the other side of your hand. Hence, there is as much space in your hand as in all the universe.

Also, nothing exists apart from those electromagnetic forces.

Not that means anything or has much use but to keep me from picking lint out of my navel.