Set Notation

From dis-Emi-A

This is a collection of common set notation which comes up a lot while creating algorithms -- mainly the ones I often forget ;) I wish I could use these all natively in a programming language (along with all the propositional logic).

Refer [Math Symbols]

|{…}| :

he cardinality (length) of the set

∴, ∵ : th

refore, because

∧, ∨, ⊕ : and,

or, xor

∀ :

niversal quantification, for all: ∀ n ∈ ℕ: n2 ≥ n.

∃ :

xistential quantification, there exists at least one: ∃ n ∈ ℕ: n is even.

∃! :

niqueness quantification: ∃! n ∈ ℕ: n + 5 = 2n.

: 

such that: {n ∈ ℕ : n2 < 20} = { 1, 2, 3, 4}

∈, ∉ : se

membership: (1/2)−1 ∈ ℕ, 2−1 ∉ ℕ

⊆, ⊂ : su

set

⊇, ⊃ : su

erset

∪ :

et-theoretic union: A ∪ B = { x : x ∈ A ∨ x ∈ B }

∩ :

ntersection: A ∩ B = { x : x ∈ A ∧ x ∈ B }

∆ :

ifference : A ∆ B = { x : x ∈ A ⊕ x ∈ B }

∖ :

ubtraction : A ∖ B = { x : x ∈ A ∧ x ∉ B } Correct?