Chapter 02 Archives - The Nature of Mathematics

Individual Research Project Section 2.5

September 28, 2015June 30, 2015 by elaine

Project 2.5

Let S be the set of all real numbers between 0 and 1. Prove that the set S is not a countable set.… See the whole entry

Individual Research Project Section 2.4

September 28, 2015June 30, 2015 by elaine

Project 2.4

Write a report discussing the creation of colors using additive color mixing and subtractive color mixing.

w10-4 … See the whole entry

Individual Research Project Section 2.3

September 28, 2015June 30, 2015 by elaine

Project 2.3

What is the millionth positive integer that is not a square, cube, or fifth power?… See the whole entry

Individual Research Projects Section 2.2

September 28, 2015June 30, 2015 by elaine

Project 2.2

What is the millionth positive integer that is not a square or a cube?… See the whole entry

Individual Research Projects Section 2.1

September 28, 2015June 30, 2015 by elaine

Project 2.1

The KenKen puzzle is an arithmetical puzzle that ties together sets, magic squares, and suduko-type puzzles.

KenKen

Each of these puzzles uses the set consisting of the first n counting numbers. The rules are simple:

Fill in the grid

… See the whole entry

Video Links 2-4

August 11, 2015June 30, 2015 by elaine

Infinity (from scratch) – slightly humorous, but mathematically correct. (time: 9:42)

The smallest Infinity (time: 9:33)
… See the whole entry

Video Links 2-1

August 11, 2015June 30, 2015 by elaine

Venn diagrams (time: 2:00)

… See the whole entry

Reference Topics 2-4

June 27, 2018June 30, 2015 by elaine

This site introduces the idea of infinite sets:
http://mathforum.org/isaac/problems/cantor1.html

This site introduces the idea that there are different sizes of infinity:
http://www.math.grinnell.edu/~miletijo/museum/infinite.html

A slightly more advanced discussion of sets can be found in the article, “A Crash course in the … See the whole entry

Reference Topics 2-3

December 12, 2016June 30, 2015 by elaine

Venn diagrams with two, three, and four sets:
If you click on the question mark, you can practice with three overlapping sets.
http://www.math.csusb.edu/notes/sets/node5.html

This site shows a statement of De Morgan’s law.
https://www.quora.com/What-is-the-significance-of-De-Morgans-Laws… See the whole entry

Reference Topics 2-2

February 11, 2018June 30, 2015 by elaine

This is a web-based instructional module on the algebra of sets.

http://www.math-only-math.com/laws-of-algebra-of-sets.html

Union of Sets:
https://www.basic-mathematics.com/union-of-sets.html

Intersection of Sets:
https://www.basic-mathematics.com/intersection-of-sets.html

Venn Diagrams for union and intersection:
https://www.mathsisfun.com/sets/venn-diagrams.html… See the whole entry