An Example of a "Learning Process" Journal (using the 2 colored box format)

Book: The Nature of Mathematics 10th ed by Karl Smith.

Source: Toronto Thomson Brooks/Cole, 2004.

It is 6:40 am (Wednesday). I am eager to continue with the math. Yesterday was a bit frustrating - I hope to return to a positive attitude this morning.

1.4 Finite and Infinite (p. 39 - 52)

• "in mathematics we use the word set to refer to any collection of objects." (p. 39)
• "The term set is undefined. Remember, the fact that we do not define set does not prevent us from having an intuitive grasp of how to use the word." (p. 39)
• there are some new terms, and some new notational conventions
  • description method (for specifying a set) - the description makes it clear whether an element is in the set or not.
  • roster method (for specifying a set) - all of the elements are listed.

I got sidetracked when I encountered some of the special notational requirements for set theory. The Word Equation Editor is not strong enough for this, but I found Math Type on the web that does the job. Now to see if I can locate a copy in the university.

Although I am presently restricted in my note making, I will continue reading the book, and making some notes...

Definitions:

• the number of elements in a set is called its cardinality.
• Two sets are called equivalent if they have the same cardinality.
• Two sets A and B are said to be in a one-to-one correspondence if we can find a pairing so that
  • each element of A is paired with precisely one element of B, and
  • each element of B is paired with precisely one element of A.
• An infinite set is a set that can be place in a one-to-one correspondence with a proper subset of itself.
• George Cantor assigned the symbol aleph-null to the cardinal number of the set of counting numbers.

I am now at the end of the first chapter.

There is now a section called the Chapter Summary which lists

• the important terms
• types of problems
• review questions.

I will have a look at this next time.

7:40 am

Mathematics Index