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Mathematics LibreTexts

Back Matter

  • Page ID
    79611
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    • Index
    • Appendix A: Relations
      A typical way to define a function f from a set S, called the domain of the function, to a set T, called the range, is that f is a relationship between S to T that relates one and only one member of T to each element of X. We use f(x) to stand for the element of T that is related to the element x of S. If we wanted to make our definition more precise, we could substitute the word “relation” for the word “relationship” and we would have a more precise definition.
    • Appendix B: Mathematical Induction
      There is a variant of one of the bijections we used to prove the Pascal Equation that comes up in counting the subsets of a set. In the next problem, it will help us compute the total number of subsets of a set, regardless of their size. Our main goal in this problem, however, is to introduce some ideas that will lead us to one of the most powerful proof techniques in combinatorics (and many other branches of mathematics), the principle of mathematical induction.
    • Appendix C: Exponential Generating Functions
      We did quite a few examples that showed how combinatorial properties of arrangements counted by the coefficients in a generating function could be mirrored by algebraic properties of the generating functions themselves. The monomials x^i are called indicator polynomials. In general, a sequence of polynomials is called a family of indicator polynomials if there is one polynomial of each nonnegative integer degree in the sequence.
    • Appendix D: Hints to Selected Problems
      This section contains the hints to selected exercise problems in this textbook.
    • Appendix E: GNU Free Documentation License

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