集合入门

在本课中，我们讨论集合的基本定义，而不深入探讨诸如集合是否可以是其自身成员之类的情况。这种人为构造的情形会导致所谓的罗素悖论。

为了解决罗素悖论，需要使用被称为ZFC公理的公理化集合定义。对于本课程的目的而言，我们不需要公理化处理，经典集合定义已足够。

S = {a, e, i, o, u}

F = {\text{apple, banana, orange, cherry, guava, apricot}}

S={e, a, u, o, i}={i, o, e, u, a}

\begin{align*} A &= {\text{horse, donkey, bull, cow, dog}}\ B & = {1, 4, 9, 16, 25, 36, 49, 64, 81}\ C & = {1, 8, 27, 64, 125, 216, 343, 512, 729}\ D & = {i, j, k, l, m, n}\ E &={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}\ F &= {\text{apple, banana, orange, cherry, guava, apricot}} \end{align*}

S = {x\mid x \text{ is a vowel character in the English alphabet}}

\begin{align*} B &= {x^2 \mid x\text{ is an integer, }0<x<10}\ E &= {x\mid x \text{ is a character in the English alphabet}} \end{align*}

O={x\mid x \text{ is an odd positive integer.}}

{9}, {0}, {\emptyset}, {\text{horse}}, {i}

\mathbb{N} = {1, 2, 3, 4, \ldots }

\mathbb{W} = {0, 1, 2, 3, 4, \ldots}

\mathbb{Z} = {0, \pm1, \pm2, \pm3, \pm 4, \ldots}

\mathbb{Q} = \left{\frac{p}{q} \mid p \text{ and } q \text{ are integers, and } q\ne 0 \right}

1A = {'horse','donkey','bull','cow','dog'}
2B = {1,4,9,16,25,36,49,64,81}
3C = {1,8,27,64,125,216,343,512,729}
4D = {'i','j','k','l','m','n'}
5E = {'a','b','c','d','e','f','g','h','i','j','k','l','m',
6'n','o','p','q','r','s','t','u','v','w','x','y','z'}
7F = {'apple','banana','orange','cherry','guava','apricot'}
8G = {'elephant',1917,'E',True,3.1417}
9print("G = " + str(G))
10print("|G| = " + str(len(G)))
11for x in G:
12    print(x)