An Introduction to Mathematical ReasoningWhat is mathematics; Symbolic logic; A reviw of number and notation; Further review topics; Introduction to proofs; Direct proof I; Direct Proog II; Indirect proof; Analogy abnd geometric proof. |
Contents
What Is Mathematics? | 1 |
Symbolic Logic | 5 |
A Review of Numbers and Notation | 23 |
Copyright | |
16 other sections not shown
Common terms and phrases
a₁ a₁x algebraic ANALOGY AND GEOMETRIC Assume axioms binomial coefficients Cauchy-Schwarz inequality clearly column common logarithms completes the proof compute consecutive integers Consider contradiction counterexample defined digits DIRECT PROOF divisible division ring equal equation equivalent example exists false Figure finite differences function f(x FURTHER REVIEW TOPICS graph HOMEWORK PROBLEMS illustrate implies indirect method inequality infinite number integer irrational number lim f(x loga logarithms mathematical induction mathematical proof mathematicians method of proof n₁ natural number nonnegative number notice obtain odd number P₁ polynomial positive numbers prime number PROBLEMS FOR CHAPTER properties proposition proves the result R₁ R₂ rain tomorrow rational number real numbers reason satisfy set of real Show Similarly square statement student summation notation symbolic logic theorem trigonometric functions true truth table universal quantifier verify x₁ y₁ zero Τ Τ Τ