Math 142A Fall 2017
Terminology and Theorems

Updated 10/3/17

• Chapter 1
  • inductive set
  • principle of mathematical induction
  • bounded above/below, bounded
  • supremum
  • infimum
  • completeness axiom
  • distribution of the integers
  • distribution of the rational numbers
  • archimedean property
  • dense
  • the set of rational numbers is dense
  • the set of irrational numbers is dense
  • triangle inequality
  • difference of powers formula
  • geometric sum formula
  • binomial formula
• Chapter 2
  • sequence
  • converge
  • comparison lemma
  • sum, product and quotient properties
  • linearity and polynomial properties
  • bounded sequence
  • sequentially dense set
  • closed set
  • monotonically increasing/decreasing, monotone
  • monotone convergence theorem
  • nested interval theorem
  • subsequence
  • every sequence has a monotone subsequence
  • every bounded sequence has a convergent subsequence
  • sequentially compact
  • sequential compactness theorem
• Chapter 3
  • continuous at x₀
  • continuous
  • composition f o g
  • image
  • maximum value
  • maximizer
  • minimum value
  • minimizer
  • extreme value theorem
  • intermediate value theorem
  • bisection method
  • convex set
  • uniformly continuous
  • ε-δ criterion at a point
  • ε-δ criterion on the domain
  • monotonically increasing/decreasing
  • monotone
  • strictly increasing/decreasing
  • strictly monotone
  • one-to-one
  • inverse
  • distinct from
  • limit point
  • limit (of a function)
• Chapter 4
  • tangent line
  • differentiable
  • derivative
  • differentiation rules
    • sum rule
    • product rule
    • quotient rule
  • derivative of inverse function
  • derivative of the composition: chain rule
  • Rolle's theorem
  • mean value theorem
  • identity criterion
  • criterion for strict monotonicity
  • local maximizer, local minimizer
  • Cauchy mean value theorem
  • Leibnitz notation