O'Reilly logo

Good Math by Mark C. Chu-Carroll

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

1Natural Numbers

What’s a number?

In math, we could answer that question a few different ways. We could answer it semantically by looking at what numbers mean. Or we could answer that question axiomatically by looking at how they behave. Or we could answer the question constructively by looking at how we could build the numbers from some other kind of simpler object.

We’ll start with semantics. What do numbers mean? We all think we know the answer to this, but in fact, we’re wrong most of the time! People think that a number is just one thing, the thing that you use to count, and that’s it. But that’s not really true. Numbers can have two different meanings, depending on how they’re used.

There are two kinds of numbers. When you see the ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required