Chapter 2 Links
Chapter 2 - Section 1 page 124: The Beginning of Set Theory
More information about the history of set theory can be found at the MacTutor History of Mathematics Archive at the University of St. Andrews, Scotland at
http://www-history.mcs.st-and.ac.uk/history/HistTopics/Beginnings_of_set_theory.html
Chapter 2 - Section 1 page 124: The Mathematical Atlas: Set Theory
More information on set theory can be found at the Mathematical Atlas site.
Chapter 2 - Section 1 page 123: George Ferdinand Ludwig Philipp Cantor
A biography and a photograph of Georg Cantor can be found at the MacTutor History of Mathematics Archive at the University of St. Andrews, Scotland, at
http://www-history.mcs.st-and.ac.uk/history/Biographies/Cantor.html
Chapter 2 - Section 1 page 125: Bertrand Arthur William Russell
A biography and a photograph of Bertrand Russell can be found at the MacTutor History of Mathematics Archive at the University of St. Andrews, Scotland, at
http://www-history.mcs.st-and.ac.uk/history/Biographies/Russell.html
Chapter 2 - Section 1 page 126: John Venn
Biographical information about John Venn can be found at the MacTutor History of Mathematics Archive at the University of St. Andrews, Scotland, at
http://www-history.mcs.st-and.ac.uk/history/Biographies/Venn.html
Chapter 2 - Section 1 page 129: Rene Descartes
Biographical information and a portrait of René Descartes can be found at the MacTutor History of Mathematics Archive at the University of St. Andrews, Scotland, at
http://www-history.mcs.st-and.ac.uk/history/Biographies/Descartes.html
Chapter 2 - Section 1 page 133: Paradoxes
You can find a collection of many intriguing paradoxes including those relating to logic and to sets, as well as paradoxes from literature, at an amusing and highly informational site. See whether you can find errors in the incorrect proofs.
https://web.archive.org/web/20060423034717/http://www.wordsmith.demon.co.uk/paradoxes/
Chapter 2 Section 1 page 133: Russell's Paradox
The on-line Stanford Encyclopedia of Philosophy contains an excellent discussion of Russell's paradox at
http://plato.stanford.edu/archives/win1997/entries/russell-paradox/
Chapter 2 Section 1 page 133: Russell's Paradox
You can also read more about Russell's paradox at the Cut-the-Knot site at
https://web.archive.org/web/20000603103709/http://www.cut-the-knot.com/selfreference/russell.html
Chapter 2 - Section 1 page 133: Paradoxes
You can find a collection of many intriguing paradoxes including those relating to logic and to sets, as well as paradoxes from literature, at this amusing and highly informational site. See whether you can find the errors in the incorrect proofs.
https://web.archive.org/web/19990302071024/http://www.wordsmith.demon.co.uk/paradoxes/
Chapter 2 – Section 2 page 133: Notes on Set Theory
Material on set theory and set operations can be found at the sties of the Department of Mathematics of the University of California of San Bernardino site at
https://web.archive.org/web/20120323182522/http://www.math.csusb.edu:80/notes/sets/sets.html
Chapter 2 - Section 2 page 133: More on Set Operations
Material on set operations can be found at the Math Notes site of the Department of Mathematics of the University of California at San Bernardino at
https://web.archive.org/web/20080702031350/http://www.math.csusb.edu:80/notes/sets/node2.html
Chapter 2 – Section 2 page 134: Venn Diagrams
A javascript applet for creating attractive Venn diagrams for union of between two and six sets can be found at
http://www.interactivenn.net/index.html
Chapter 2 - Section 2 page 143: Bhaskaracharya
Biographical information on Bhaskaracharya can be found at
Chapter 2 – Section 2 page 146: Fuzzy Logic
Information about fuzzy logic and sets can be found at
https://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol2/jp6/article2.html
and at
Chapter 2 - Section 3 page 158: Floor Function
To learn more about the floor and ceiling functions, go to
http://en.wikipedia.org/wiki/Floor_function
Chapter 2 - Section 3 page 159: Floor Function
For more information about the identity in Example 31 (and its generalizations), go to
https://en.wikipedia.org/wiki/Hermite%27s_identity
Chapter 2 - Section 4 page 167: Fibonacci sequence
Information about the Fibonacci sequence can be found in many places on the Internet and in many books. We will also return to this subject later in the text (see Chapters 5 and 8). One of the many web sites on the Fibonacci numbers is
https://en.wikipedia.org/wiki/Fibonacci_number
Chapter 2 – Section 4 page 167: Fibonacci
Biographical information about Fibonacci can be found at
https://learnodo-newtonic.com/fibonacci-facts and at the MacTutor site at
http://www-history.mcs.st-andrews.ac.uk/Biographies/Fibonacci.html
Chapter 2 - Section 4 page 171: Neil Sloane (Home Page)
For more information about Neil Sloane and his many activities and interests consult http://neilsloane.com/
Chapter 2 - Section 4 page 172: The
Online Encylcopedia of Integer Sequences
site, developed by Neil Sloane at AT&T Labs and now supported by the OEIS foundation, can be used to determine the possible identity of an integer sequence from its first few terms. To use the site for this purpose, enter the first few terms of a sequence and click to get feedback on which sequence or sequences may be the sequence of interest. This site also offers the opportunity to check out some ""hot sequences"" and offers some puzzle sequences that are quite challenging. You can access an introduction to this site at
https://www.maa.org/sites/default/files/pdf/upload_library/22/Robbins/Sloane-Robbins.pdf
and you can access the site at
https://oeis.org/
Chapter
2 - Section 4 page 178 (exercise 20): World Population Growth
The growth rate of the population of the world is actually projected to decrease. For the latest view, consult
https://ourworldindata.org/world-population-growth
Chapter 2 - Section 4 page 178: Exercise 20
Information about the current and forecasted population of the world can be found at
http://www.worldometers.info/world-population/#table-forecast
Chapter 2 - Section 4 page 178 (exercise 24): Amortization Calculator
You can find an applet that can calculate loan payments, and other quantities, at
http://www.amortization-calc.com/
Chapter 2 - Section 4 page 178: Exercise 24
To learn more about how to calculate the remaining balance of a loan consult
http://www.financeformulas.net/Remaining_Balance_Formula.html
Chapter 2 - Section 5 page 181: Hilbert’s Grand Hotel
To learn more about Hilbert’s Grand Hotel consult
http://mathandmultimedia.com/2014/05/26/grand-hotel-paradox/
or at
https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel
It is not currently possible to book a room at Hilbert’s Grand Hotel on the web, even though there are always rooms available.
Chapter 2 - Section 5 page 181: Hilbert
Biographical information on David Hilbert can be found at
https://www.britannica.com/biography/David-Hilbert
or at the MacTutor site at http://www-groups.dcs.st-and.ac.uk/history/Biographies/Hilbert.html
Chapter 2 - Section 5 page 183: Cantor's diagonal argument
You can read about Cantor's diagonalization argument in this Wikipedia article.