Introduction to Infinitesimal Analysis: Functions of One Real Variable

a₁ approached by f(x approaches zero axiom b₁ b₂ bound of f(x bounded function change sign content zero continuous function convergent corresponding defined denoted E. H. MOORE Engineering equal equation exists a V*(a f(x)dx exists f(x+nh f₁(x fi(x finite number finite set function f(x greatest lower bound Hence hypothesis improper definite integral improper integral infinite series infinitesimal integers integral exists integral of f(x interval a b irrational number Large 12mo least upper bound lemma limit point monotonic function multiple-valued functions necessary and sufficient neighborhood of x=a oscillation of f(x P₁ partition point x₁ positive integers positive number prove rational numbers less real numbers segment a b sequence set of numbers set of points set of segments Si(x)dx subset sufficient condition Theorem 26 Theorem 40 tion uniformly continuous value approached values of f(x x)dx x₁ and x2 y₁