GREEK ALPHABET (Capitals in brackets)
a : alpha (A) i : iota (I) r : rho (R)
b : beta (B) k : kappa (K) s : sigma (also V) (S)
g : gamma (G) l : lambda (L) t : tau (T)
d : delta (D) µ : mu (M) u : upsilon (U)
e : epsilon (E) n : nu (N) j : phi (F)
z : zeta (Z) x : xi (X) c : chi (C)
h : eta (H) o : omicron (O) y : psi (Y)
q : theta (Q) p : pi (P) w : omega (W)
SET THEORY
Î : “is an element of” ℤ : Integers ½ ½ : cardinality (size)
Ï : “not an element of” ℤ+ : Positive Integers ½ : “such that” (*)
Ç : Intersection ℤ -
: Negative Integers “:” : “such that” (*)
È : Union ℝ : Reals ´ : Cartesian (Cross) Product
Í : Subset ℝ +
: Positive Reals \ : Set Exclusion
Ì : Strict/Proper Subset ℝ -
: Negative Reals r : Symmetric Difference
Ê : Superset ℚ : Rational Numbers Ä : Tensor Product
É : Strict Superset ℚ +
: Positive Rationals (x, y) : open interval (*)
ℚ- : Negative Rationals [x, y] : closed interval
Æ : Empty Set (*)
{ } : Empty Set (*) ℕ : Natural Numbers (x, y] : open-closed interval
ℕ : Positive Naturals (*)
*
[x, y) : closed-open interval
ÃX : Power Set of X (*)
2X : Power Set of X (*) ℕ : Positive Naturals (*)
+
Set Notation : { xÎX | “condition on x”} – The subset of X that satisfies the condition.
Cartesian Product : A ´ B = { (x, y) | xÎA, yÎB } – The set of ordered pairs from A and B.
Power set of X : ÃX = { S | S Í X } = 2X – The set of subsets of X.
Note : {{}} ¹ Æ ¹ {Æ}
BINARY OPERATORS
< : less than ³ : greater than or equal to ½ : Divides (*)
> : greater than ¹ : Not Equal » : Approximately Equal to
£ : less than or equal to º : Equivalence
LOGICAL OPERATORS & QUANTIFIERS
" : ”for all” ® : Logical Implication (*) ¬ : Negation
$ : “there exists” « : 2 way Logical Imp’n (*) Å : Exclusive Or
Ù : “and” Û : “if and only if” (*)
Ú : “or” Þ : implication (*)
MISCELLANEOUS
∴ : “therefore” : floor function [ xR ] : Equivalence class of x
∵ : “because” : ceiling function with respect to R
+
¥ : infinity : angled brackets ,-. 𝑓(𝑖) : summation from
ƒ : function ( ) : round brackets i=1 to n of f(i)
° : composite function [ ] : square bracket 0∈2 𝑓(𝑥) : summation over X
± : plus or minus { } : curly brackets of f(x)
! : factorial (x, y) : ordered pair (*)
𝑓: 𝐴 → 𝐵, 𝑥 ↦ 𝑓(𝑥)
The function f maps from the set A (Domain) to the set B (Codomain),
such that xÎA maps to f(x)ÎB.
*Note the similarities between Æ & {}, ℕ+ & ℕ*, ‘½’ & ‘:’, ÃX & 2X, ® & Þ, « & Û, divides &
such that (‘|’), and also between the open interval and the ordered pair (“(x, y)”). All symbols must be
taken in context and may be interchanged between different sources and texts.
