## Pure Theory of One-Variable Calculus:

Thread #1: Preliminaries

axiom: the parallel postulate

definition: Jordan curve

definition: polygon, n-gon

definition set: names for n-gons for n = 3 to 10

definition: trapezoid

definition: convex region

theorem: sum of the interior angles of an n-gon

theorem: number of diagonals of a convex n-gon

definition: R (= the set of real numbers)

theorem: the quadratic formula

definition: absolute value

theorem set: properties of absolute value

definition: symmetry about an axis

definition: symmetry about a point

definition of a function

definition: an odd function

definition: an even function

definition: reflection about an axis

definition: Z (= the set of integers)

well-ordering axiom

theorem: principle of mathematical induction

definition: divisor

definition: prime

definition: factorial

theorem: the number of primes is infinite

theorem: formula for the number of permutations of n things taken r at a time

theorem: formula for the number of combinations of n things taken r at a time

definition: Q (= the set of rational numbers)

definition: summation notation

definition: string (= finite sequence)

theorem: the telescoping property for finite sums

definition: arithmetic mean

theorem: formula for the arithmetic mean

definition: arithmetic progression

theorem: sum of the terms of an initial segment of an arithmetic progression

definition: geometric mean

theorem: formula for the geometric mean

preview: the relationship between the geometric mean and the arithmetic mean

definition: geometric progression

theorem: sum of the terms of an initial segment of a geometric progression

theorem: sum of a geometric series

theorem: connection between arithmetic progressions and geometric progressions

definition: harmonic mean

theorem: travel time, given constant speeds over distances

theorem: HA = G2

axiom: Mamikon’s theorem

theorem: formula for the area between two concentric circles, in terms of their secant-tangent

the Pythagorean Theorem

(end of page)

definition: Jordan curve

definition: polygon, n-gon

definition set: names for n-gons for n = 3 to 10

definition: trapezoid

definition: convex region

theorem: sum of the interior angles of an n-gon

theorem: number of diagonals of a convex n-gon

definition: R (= the set of real numbers)

theorem: the quadratic formula

definition: absolute value

theorem set: properties of absolute value

definition: symmetry about an axis

definition: symmetry about a point

definition of a function

definition: an odd function

definition: an even function

definition: reflection about an axis

definition: Z (= the set of integers)

well-ordering axiom

theorem: principle of mathematical induction

definition: divisor

definition: prime

definition: factorial

theorem: the number of primes is infinite

theorem: formula for the number of permutations of n things taken r at a time

theorem: formula for the number of combinations of n things taken r at a time

definition: Q (= the set of rational numbers)

definition: summation notation

definition: string (= finite sequence)

theorem: the telescoping property for finite sums

definition: arithmetic mean

theorem: formula for the arithmetic mean

definition: arithmetic progression

theorem: sum of the terms of an initial segment of an arithmetic progression

definition: geometric mean

theorem: formula for the geometric mean

preview: the relationship between the geometric mean and the arithmetic mean

definition: geometric progression

theorem: sum of the terms of an initial segment of a geometric progression

theorem: sum of a geometric series

theorem: connection between arithmetic progressions and geometric progressions

definition: harmonic mean

theorem: travel time, given constant speeds over distances

theorem: HA = G2

axiom: Mamikon’s theorem

theorem: formula for the area between two concentric circles, in terms of their secant-tangent

the Pythagorean Theorem

(end of page)