List of mathematical symbols
Symbols based on equality

List of mathematical symbols

Section Title: Symbols based on equality
Table Section Text: None

Symbol in HTML	Symbol in TeX	Name	Explanation	Examples

Read as

Category

=	equality is equal to; equals everywhere	means and represent the same thing or value.

≠	\ne	inequality is not equal to; does not equal everywhere	means that and do not represent the same thing or value. (The forms !=, /= or are generally used in programming languages where ease of typing and use of ASCII text is preferred.)

≈	\approx	approximately equal is approximately equal to everywhere	x ≈ y means x is approximately equal to y. This may also be written ≃, ≅, ~, ♎ (Libra Symbol), or ≒.	π ≈ 3.14159

isomorphism is isomorphic to group theory	G ≈ H means that group G is isomorphic (structurally identical) to group H. (≅ can also be used for isomorphic, as described below.)	Q8 / C2 ≈ V

~	\sim	probability distribution has distribution statistics	X ~ D, means the random variable X has the probability distribution D.	X ~ N(0,1), the standard normal distribution

row equivalence is row equivalent to matrix theory	A ~ B means that B can be generated by using a series of elementary row operations on A

same order of magnitude roughly similar; poorly approximates; is on the order of approximation theory	m ~ n means the quantities m and n have the same order of magnitude, or general size. (Note that ~ is used for an approximation that is poor, otherwise use ≈ .)	2 ~ 5 8 × 9 ~ 100 but π2 ≈ 10

similarity is similar to geometry	△ABC ~ △DEF means triangle ABC is similar to (has the same shape) triangle DEF.

asymptotically equivalent is asymptotically equivalent to asymptotic analysis	f ~ g means.	x ~ x+1

equivalence relation are in the same equivalence class everywhere	a ~ b means (and equivalently ).	1 ~ 5 mod 4

=: := ≡ :⇔ ≜ ≝ ≐	\equiv :\Leftrightarrow \triangleq \overset{\underset{\mathrm{def}}{}}{=} \doteq	definition is defined as; is equal by definition to everywhere	x := y, y =: x or x ≡ y means x is defined to be another name for y, under certain assumptions taken in context.

≅	\cong	congruence is congruent to geometry	△ABC ≅ △DEF means triangle ABC is congruent to (has the same measurements as) triangle DEF.

isomorphic is isomorphic to abstract algebra	G ≅ H means that group G is isomorphic (structurally identical) to group H. (≈ can also be used for isomorphic, as described above.)	V ≅ C2 × C2

≡	\equiv	congruence relation ... is congruent to ... modulo ... modular arithmetic	a ≡ b (mod n) means a − b is divisible by n	5 ≡ 2 (mod 3)

identical equality is identically equivalent to mathematical analysis	for two functions f, g, means for all x.

⇔ ↔	\Leftrightarrow \iff \leftrightarrow	material equivalence if and only if; iff propositional logic	A ⇔ B means A is true if B is true and A is false if B is false.	x + 5 = y + 2 ⇔ x + 3 = y

:= =:	Assignment is defined to be everywhere	A := b means A is defined to have the value b.	Let a := 3, then... f(x) := x + 3

Sentence(s)

The equals sign (=) is a mathematical symbol used to indicate equality.

final_sentence: The equals sign (=) is a mathematical symbol used to indicate equality.