| 释义 |
SetA set is a Finite or Infinite collection of objects. Older words for set include Aggregate andClass. Russell also uses the term Manifold to refer to a set. The study of sets and theirproperties is the object of Set Theory. Symbols used to operate on sets include  (which denotes theEmpty Set  ),  (which denotes the Power Set of a set),  (which means ``and'' orIntersection), and  (which means ``or'' or Union).
The Notation  , where  and  are arbitrary sets, is used to denote the set of Maps from to. For example, an element of  would be a Map from the Natural Numbers to the set  . Call such a function  , then  ,  , etc., are elements of , so call them  ,  ,etc. This now looks like a Sequence of elements of , so sequences are really just functions from to . This Notation is standard in mathematics and is frequently used in symbolic dynamics to denote sequence spaces.
Let  ,  , and  be sets. Then operation on these sets using the and operators is Commutative
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 runs through any Index Set  . The proofs follow trivially from the definitions of union andintersection.
The table below gives symbols for some common sets in mathematics.
| Symbol | Set |  |  -Ball |  | Complex Numbers |  ,  | -Differentiable Functions |  | -Disk |  | Quaternions |  | Integers | | Natural Numbers |  | Rational Numbers |  | Real Numbers in -D |  | -Sphere |  | Integers |  | integers (mod ) |  | Negative Integers |  | Positive Integers |  | Nonnegative Integers |
References
Courant, R. and Robbins, H. ``The Algebra of Sets.'' Supplement to Ch. 2 in What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 108-116, 1996.
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