CHANGES

Version 2.0  (9/2010) Initial version released with hardcopy also available through Lulu.com.
  A huge number of typos were corrected and many new exercises added.

Version 2.1  (5/2012) 
  Page xviii "Principle" -> "Principal"
  Page 361  Fixed mangled equation near bottom of page. 
  Put exercises into seperate files
  In Section 2.3 exercise 7 part b: proof was entirely wrong.
  Exercise #9 in Section 3.3 the hypotheses should have included that the
real numbers a,b,c and d are positive.
  Exercise #7 in Section 3.5 The correct number of integers in [1,100] that
can't be written using fewer than 4 squares is 15 (not 17).
  Exercise #9 in Section 5.3 The statement had a typo, the correct statement
to prove is 6|(2n^3 - 2n - 12).

Version 3.0 (12/2012)
  Dealt with the whole "Is 0 in the Naturals?" issue.
  Fixed many typographical errors.
  Reformatted to allow for creating a workbook for exercises.
  Fixed errors in several exercises:
    Exercise #7 (part b) in Section 2.3.
    Exercise #9 in Section 3.3.
    Exercise #7 in Section 3.5.
    Exercise #9 in Section 5.3. 

Version 3.1 (1/7/2014)

Added boolean switches to allow creating the text, a workbook and the hints/solutions guide all
using the same source files.

Added boolean switches to allow for four versions: plain, S, N and SN.  The S flag means that logical
negation is denoted using $\sim$ rather than $\lnot$.  The N flag distinguishes a version in which
the convention that $1$ is the smallest natural number is followed throughout.  The absence
of the N flag indicates the original version of the text in which the naturals do not contain $0$
in chapters 1 through 4 and (after the Peano axioms are introduced) that convention is changed
to the more modern rule. 

Reorganized source files into subdirectories for each chapter.

Repaired a major gaff in the discussion of  the quantification status of P(k) in proving \forall k, P(k)=>P(k+1)

Added double negation laws (resp. double complementation) to Logic and Set Theory sections (esp. the 
tables summarizing the rules).

Fixed several German language typos noticed by Karl-Dieter Crisman from Gordon College.

Added a short discussion on which axioms are acceptable for use at the end of the first "proofs" chapter.


Version 3.2 (1/7/2015)

Included typo fixes and exercise suggestions from my Spring 2014 class.

Made lots of changes to improve the generation of text, workbbok and solutions manual from the same source files.

Hints on exercises now go up to section 5.2.