Assumed knowledge

• when elements can be listed, a set is said to be countable
• [a,b) = {x is an element of R : a </= x < b
• S and T are disjoint if the intersect of S and T is the empty set
• a subsequence of {Xk} is an infinite subset of the elements, in the same order
• a set is closed if and only if its complement is open (a closed set contains its boundary)
• a subset of R^n is compact if and only if it is closed and bounded
• Bolzano-Weierstrass theorem: if S is a compact subset of R^n, then every sequence of points in S has a subsequence that converges to a point in S
• [a,b] is closed, bounded and convex
• (a,b) is open, bounded and convex
• (a,b] is neither open nor closed but is bounded and convex
• if S is bounded above, then there is an upper bound b* such that if b is an upper bound for S, b*<=b and is called the supremum, or the least upper bound
• inf(S) is the infimum or the greatest lower bound
• f: S -> T

  S is the domain of the function, and T is the range
• monotonic means increasing or decreasing
• any strictly monotonic function has an inverse
• Weierstrass theorem - a continuous function f: S -> R where S is a compact subset of R, attains a maxmimum and minimum value on S
• when a Taylor series converges, it is the Taylor expansion of f about a