Zero and Infinity

My Hero, Zero

You're here,

And nobody really knows

How wonderful you are.

Why we could never reach the star,

Without you, Zero, my hero,

Zero, how wonderful you are.

When we talk about zero or infinity, we should understand what is meant by these terms.

Zero is not just the smallest number.  It is the smaller than the smallest number that can be imagined.  The smallest observable length is the Planck Length, which is  1.62× 10-35 meters.  At the speed of light, it would take  3.34 times 10-9 seconds.  Zero length is even shorter than this length. Zero time is even shorter than this time.   

At the other extreme, infinity is not just the largest number, It is larger than the largest number that can be imagined.  If the Planck length is the smallest observable number, then the inverse of the Planck length, is 6.17 times  1034 meters, which is 1.7 times 1020 light years.  This also means that  it would that it would take 1.7 times 1020  years to travel this distance  at the speed of light.  An infinite length is even large than this length, and infinite time is larger than this time.

Zero and infinity are necessary for mathematics.  But just because something is a large number it does not mean that it is infinite.  Even if something is a small number, it is still greater than zero.  Whenever we deal with large or small numbers it is important to remember this.