There is so much to say about nothing. Choosing nothing breaks false dilemmas. This or that? None for me, thanks.
Some of my favorite books about math, such as Seife’s Zero: The Biography of a Dangerous Idea, were written with zero as the main topic. Earlier this year, Amir Aczel published an account of his search for the earliest appearance of zero.
This is not an attempt to cover all of the ground there is to cover with nothing. Instead, this is a quick foray into zero as a power.
As with many worthwhile endeavors, this one starts with a question.
Why does 20 = 1?
We have learned that an exponent tells us how many times to multiply a number by itself.
We have also learned that division undoes multiplication. As the power decreases by 1, 2 to the n gets divided by 2.
Take one more step: 1 – 1 = 0 and 2/2 = 1. Therefore, 20 = 1.
Zero is a powerful force.
You don’t have to stop at nothing.
The same logic will show you how to evaluate 2–1.