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.
- Basic taxonomy -- provide quick intuitive definitions for each of the following types of number.
- Natural number
- Rational number
- Irrational number
- Transcendental number
- Real number
- Complex number
- Explain at least one thing-you-didn't-already-know about each type of number.
- [45h $~$\mathbb N$~$]:
- History of zero
- Definition from successor function
- [48l $~$\mathbb Z$~$]:
- History of negative numbers
- [4zq $~$\mathbb Q$~$]:
- Did you know that there are the same number of rational numbers as there are integers?
- [54z $~$\mathbb I$~$]:
- Transcendental numbers:
- ?? %%note: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.%%
- [4bc $~$\mathbb 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?
- [4zw $~$\mathbb C$~$]:
- 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.
Much of the work has already been done -- we have pages on each of these types of number. Two main pieces of work remaining:
Polish the existing pages up to A-class or B-class (including testing the explanations on Math 1/2 readers and incorporating feedback.)
Add pages/lenses for the various things-you-didn't-already-know.