Cambridge International AS and A Level Mathematics
Mathematical notation
Examinations for CIE syllabuses may use relevant notation from the following list.
1 Set notation
∈ is an element of
∉ is not an element of
{x1, x2, …} the set with elements x1, x2, …
{x : …} the set of all x such that …
n(A) the number of elements in set A
∅ the empty set
the universal set
, the universal set (for 0607 IGCSE International Mathematics)
A′ the complement of the set A
ℕ the set of natural numbers, {1, 2, 3, …}
ℤ the set of integers, {0, ±1, ±2, ±3, …}
ℚ the set of rational numbers,
ℝ the set of real numbers
ℂ the set of complex numbers
(x, y) the ordered pair x, y
⊆ is a subset of
⊂ is a proper subset of
⋃ union
⋂ intersection
[a, b] the closed interval {x ∈ ℝ : a ⩽ x ⩽ b}
[a, b) the interval {x ∈ ℝ : a ⩽ x < b}
(a, b] the interval {x ∈ ℝ : a < x ⩽ b}
(a, b) the open interval {x ∈ ℝ : a < x < b}
(S, ∘) the group consisting of the set S with binary operation ∘
2 Miscellaneous symbols
= is equal to
≠ is not equal to
≡ is identical to or is congruent to
≈ is approximately equal to
~ is distributed as
≅ is isomorphic to
∝ is proportional to
< is less than
⩽ is less than or equal to
> is greater than
⩾ is greater than or equal to
∞ infinity
⇒ implies
⇐ is implied by
⇔ implies and is implied by (is equivalent to)
