# 離散數學

## 集合
* Definition 1
A set is an unordered collection of object

a = {1, 3, 5} # is a set
b = {4, 3, 5} # is a set
c = {1, 5, 3} # is a set

a = c # 無順序性

* Definition 2
The object in a set are colled, the element, or the members, if the set.
A set is said to contain ite element.
If an element x is belong to a set A, then we denote it by x ∈ A

o = {1, 2, 3, 4, 5}
o = {x | .......} # => is range(1, 5) //


# another way to describe a set is to use set builder notation.
a = {1, 3, 5, 7, 9}
o = {x | is an odd positive intger less than 10}



o = {x ∈ z+ | x is odd and x < 10} 

* other example

# The set of integers:
z = {...-2, 0, ....}

# The set of positive integers:
z+ = {1, 2, 3...}

# The set of non-negative intergers:
z+(加號底下有0) = {0, 1, 2, 3}

# The set of rational numbers
Q = {p / q | p ∈ Z, q ∈ Z, and Q != 0}


* Definition 3
Two sets are equal
:::danger
if only if they have the same element. That is, if A and B are sets, than A and B are equal if and only if
:::

* 集合
* Definition 7
* 0

* example 7
* one - to - one (到這)

* example 8

* example 9

* note
* &&

* one - to - one

* defination 6
* 廣義遞增
* 遞增遞減

* defination 7

* example 12

* example 13(使用定義 by defination onto function)

* example 14(not onto)

* defination 8

* example 16

* one - hence

* note

* defination 9

* 嚴謹寬鬆

* 合成函數與連鎖率

* 2.5
* defination 2
* 證明無窮可數
* example 3
* 可數
* example 4
* 數羊
## chapter 3
* example 1
* 0.0
* example 3
* example 5