O'Reilly logo

Advanced Mathematics for Applications by Andrea Prosperetti

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

 

Appendix

We collect here several definitions and properties which have been referred to repeatedly in the previous pages. We try to avoid unnecessary generality focusing on the aspects of specific relevance to our subjects.

A.1 Sets

A set is any well-defined collection of objects which, in our cases, have a mathematical nature. A set is typically given by enumerating all its elements or by formulating a membership criterion. Here are some properties and definitions:

  1. Empty set: This is the unique set containing no elements and is denoted by Ø.
  2. Countable set: Contains either a finite or a countably infinite number of elements.
  3. Equal sets: Both sets contain exactly the same elements.
  4. Disjoint sets: The two sets have no elements in common. ...

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