1. set is no set order without duplication, {} {} {} is not equal, since the latter contains an element
2. define sets
(1) directly to the elements enumerated
(2) define a common set of existing subset
The element must meet the specified properties, such as x is a natural number;
Use interval, such as [1,5] = {1,2,3,4,5}
Derived set of integers, such as 3z + 1 = {3x + 1: x∈Z}
(3) in conjunction with already existing collection
union(U)
intersection(∩)
complement representation as A c power, x is contained in the corpus, it is not included in A
A and B are disjoint if A∩B = ∅
sest difference(A \ B) a but not b
symmetric difference(A⊕B) a and not b or b and not a, A⊕B = (A\B)∪(B \A)
X is the number of elements represented as | X |, | Pow (x) | 2 is always equal to | x | power
3. subset S ⊆ T, comprising T ⊆ T
Subset S ⊂ T, S ⊆ T and S 6 = T
∅ is a subset of any set of
Positive integer ⊂N⊂Z⊂Q⊂R
! ! ! Note molecules from elements of the concept set, a ∈ {a, b}, a not ⊆ {a, b}; {a} ⊆ {a, b}, {a} is not ∈ {a, b}
4. power set pow(x)={A:A⊆ X}
pow(∅)={∅}
pow (pow (∅)) = ∅ {{}} ∅
5. | others | = | A | + | B | - | A∩B |
| Others | + | A∩B | = | A | + | B |
|A\B|=|A|-|A∩B|
| A⊕B | = | others | - | A∩B | = | A + B | -2 | A∩B |
6. formal language:empty word — λ
7. x * x is a series of zero or more words from a group of words
A = {aa, bb}, A * = {λ, aa, bb, aaaa, aabb, bbaa, bbbb, aaaaaa, ...}
8.
