Edwin E. Moise
City University of New York
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Archive | 1982
Edwin E. Moise
Let A and B be sets. If A ~ B′ ⊂ B, for some B′, then we write A ≤ B. If A ≤ B, but A ≁ B, then we write A < B.
Archive | 1982
Edwin E. Moise
Every continuous function [a,b] →ℝ is uniformly continuous. There are three natural proofs of this theorem, using (a) The Nested Interval Theorem, (b) the Heine-Borel Theorem, and (c) the Bolzano-Weierstrass Theorem respectively.
Archive | 1982
Edwin E. Moise
We shall use the standard terms and notations of analysis and set theory. (Thus much of the following has already appeared in the first few pages of Analysis.) ℝ is the set of all real numbers, and ℤ is the set of all integers. If A is a set, then x ∈ A means that x belongs to A. If x does not belong to A, then we write x ∉ A. Let S be a set. Then n n
Archive | 1982
Edwin E. Moise
Archive | 1982
Edwin E. Moise
left{ {xleft| {x; in ;s;and;left( ldots right)} right.} right}
Archive | 1982
Edwin E. Moise
Archive | 1982
Edwin E. Moise
n ndenotes the set of all elements of S that satisfy the condition (…). Thus the union of two sets A and B is n n
Archive | 1982
Edwin E. Moise
Archive | 1982
Edwin E. Moise
A; cup ;B; = ;left{ {xleft| {x; in ;A;or,x, in ;B} right.} right}.
Archive | 1982
Edwin E. Moise