diff options
Diffstat (limited to 'set-theory.html.markdown')
| -rw-r--r-- | set-theory.html.markdown | 10 |
1 files changed, 6 insertions, 4 deletions
diff --git a/set-theory.html.markdown b/set-theory.html.markdown index ae8b5388..144b4bbf 100644 --- a/set-theory.html.markdown +++ b/set-theory.html.markdown @@ -2,7 +2,9 @@ category: Algorithms & Data Structures name: Set theory contributors: + - ["Andrew Ryan Davis", "https://github.com/AndrewDavis1191"] --- + Set theory is a branch of mathematics that studies sets, their operations, and their properties. * A set is a collection of disjoint items. @@ -13,11 +15,11 @@ Set theory is a branch of mathematics that studies sets, their operations, and t * the union operator, `∪`, pronounced "cup", means "or"; * the intersection operator, `∩`, pronounced "cap", means "and"; * the exclusion operator, `\`, means "without"; -* the compliment operator, `'`, means "the inverse of"; +* the complement operator, `'`, means "the inverse of"; * the cross operator, `×`, means "the Cartesian product of". ### Qualifiers -* the colon qualifier, `:`, means "such that"; +* the colon, `:`, or the vertical bar `|` qualifiers are interchangeable and mean "such that"; * the membership qualifier, `∈`, means "belongs to"; * the subset qualifier, `⊆`, means "is a subset of"; * the proper subset qualifier, `⊂`, means "is a subset of but is not equal to". @@ -59,7 +61,7 @@ Long lists may be shortened with ellipses as long as the context is clear. For e Set builder notation is a more descriptive way of constructing a set. It relies on a _subject_ and a _predicate_ such that `S = { subject : predicate }`. For example, ``` -A = { x : x is a vowel } = { a, e, i, o, u, y} +A = { x : x is a vowel } = { a, e, i, o, u } B = { x : x ∈ N, x < 10 } = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 } C = { x : x = 2k, k ∈ N } = { 0, 2, 4, 6, 8, ... } ``` @@ -87,7 +89,7 @@ D = { 2x : x ∈ N } = { 0, 2, 4, 6, 8, ... } ## Special Sets ### The Power Set -* Let `A` be any set. The set that contains all possible subsets of `A` is called a "power set" and is written as `P(A)`. If the set `A` contains `n` elements, then `P(A)` contains `2^N` elements. +* Let `A` be any set. The set that contains all possible subsets of `A` is called a "power set" and is written as `P(A)`. If the set `A` contains `n` elements, then `P(A)` contains `2^n` elements. ``` P(A) = { x : x ⊆ A } |