O'Reilly logo

How to Think Like a Mathematician by Kevin Houston

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

CHAPTER 31

image

Equivalence relations

image

All animals are equal, but some animals are more equal than others.

George Orwell, Animal Farm, 1946

In this chapter we see how mathematics becomes abstracted, that is, we identify some property that we like from an example and then make a general definition that covers this example but also allows us to investigate a far wider group of objects. In Chapter 29, Modular arithmetic, we took the idea that two numbers were equivalent if they had the same remainder on division by n. Now we are going to abstract the whole ...

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