Project proposal: Intro to numbers

The purpose of this page is to sketch out what an Intro to Numbers project might look like, so we can evaluate whether it would make a good project.

Goal of the project

• Provide a guide to numbers that would be enlightening to Math 1 and Math 2 readers.

Outline

1. Basic taxonomy -- provide quick intuitive definitions for each of the following types of number.

   • Natural number
   • Integer
   • Rational number
   • Irrational number
   • Transcendental number
   • Real number
   • Complex number

2. Explain at least one thing-you-didn't-already-know about each type of number.

• $N$:
  • History of zero
  • Definition from successor function
• $Z$:
  • History of negative numbers
• $Q$:
  • Did you know that there are the same number of rational numbers as there are integers?
• $I$:
  • ??
• Transcendental numbers:
  • ?? ^[1]
• $R$:
  • Did you know that although there are the same number of rational numbers as natural numbers, there are provably more real numbers than rational numbers?
• $C$:
  • http://simplifience.com/sample/identity.html

3. Exercises to test of understanding of each type of number.

• Set of questions where a number is presented, and the reader has to say which type it belongs to.

Plan

Much of the work has already been done -- we have pages on each of these types of number. Two main pieces of work remaining:

1. Polish the existing pages up to A-class or B-class (including testing the explanations on Math 1/2 readers and incorporating feedback.)

2. Add pages/lenses for the various things-you-didn't-already-know.

1. ^{^︎}

   Eric Rogstad notes that he, as a Math 2 reader (engineering major, professional programmer), recently realized that he didn't know the difference between an irrational number and a transcendental number. (And a quick survey indicates that the rest of the development team also doesn't know the difference.) So it should be easy to find something to say that's new for Math 2 readers.