Advice on the Writing Projects for Chapter 1

1. Search your library's on-line catalog for a book with the word "fuzzy" in the title. You might find [BaGo], [DuPr], [Ka], [Ko3], [McFr], or [So], for example. The Rosen Web Site's Chapter 1 links have some sites relevant to this topic.

2. Martin Gardner and others have written some books that annotate Carroll's writings quite extensively. Lewis Carroll has become a cult figure in certain circles. See also [Ca1], [Ca2], and [Ca3] for original material.

3. A classic source here is [Wi1]. It gives a very readable account of many philosophical issues in the foundations of mathematics, including the topic for this essay. The Stanford Encyclopedia of Philosophy has a Web page on Russell's paradox. So do Francis Moorcroft and a fascinating site called Cut-the-Knot.

4. Our list of references mentions several history of mathematics books, such as [Bo4] and [Ev3]. You should also browse the shelves in your library, around QA 21.

5. This reference work is available in book form ([Sl]), but there is also an on-line version of it on the Web. Give it a try -- it's amazing!

6. Be careful when consulting books on this subject. Many of them have errors! (Popular writers sometimes do not understand the subtle issues in such things as the definition of the sequence of alephs.) On the less technical side, [Ru] has some interesting things to say on the general topic of infinity, and [Ma4] received very nice reviews. For more depth, see books on set theory (such as [Ha1]), or try [Wi1]. As with most mathematical topics, a keyword search on the Web will probably produce useful information; we found one here.

7. Transcendental numbers are in some sense the most irrational of the irrational numbers. Most real numbers fall into this category. Surprisingly, there are very simple questions in this area that are still unsolved. For example, how would one go about proving or disproving that "pi plus e" is irrational, let alone transcendental? A good place to start is [Ni]. There should also be some material in [Ma3]. The CRC Concise Encyclopedia of Mathematics has a good Web site on this topic.

8. The original is [Ba2]. Good history of mathematics books would be a place to follow up.