GlyphIndexMath symbols and operators
Copy signs for arithmetic, sets, logic, and geometry. Read what each symbol means and compare commonly confused operators.
Plus-minus sign
The plus-minus sign ± gives two possible values or a tolerance, as in 80 ± 2 mm. State which meaning you intend.
DetailsMultiplication sign
The multiplication sign × joins factors in a calculation or dimensions in a measurement. It is a different character from the letter x.
DetailsDivision sign
The division sign ÷ separates a dividend from its divisor, as in 24 ÷ 6 = 4. Use parentheses when either side contains a longer expression.
DetailsNot-equal sign
The not-equal sign ≠ says that two values or expressions are different. It does not say how far apart they are.
DetailsLess-than-or-equal sign
The less-than-or-equal sign ≤ includes the upper limit: x ≤ 12 means that 12 is allowed, as well as smaller values.
DetailsGreater-than-or-equal sign
The greater-than-or-equal sign ≥ includes the lower limit. A width of 240 mm meets a requirement written as width ≥ 240 mm.
DetailsInfinity symbol
The infinity symbol ∞ describes something unbounded, often in a limit or interval. Its mathematical meaning depends on the expression around it.
DetailsSquare-root sign
The square-root sign √ introduces the principal square root. In plain text, parentheses show how much of the expression is under the root.
DetailsSummation sign
The summation sign ∑ means to add a set of terms. It is an operator, separate from the Greek capital letter sigma Σ.
DetailsProduct sign
The product sign ∏ means to multiply a set of factors. It is distinct from the Greek capital letter pi Π and the multiplication sign ×.
DetailsIntegral sign
The integral sign ∫ introduces an integral. Write the expression to integrate, the variable, and any limits alongside it.
DetailsPartial-derivative sign
The partial-derivative sign ∂ shows differentiation with respect to one variable while others are held fixed, as in ∂f/∂x.
DetailsNabla sign
Nabla ∇ appears in gradient, divergence, and curl notation. A dot or cross after it changes the operation being described.
DetailsIncrement sign
The increment sign ∆ can label a change, such as ∆t. It looks like Greek capital delta Δ but has a different code point.
DetailsApproximately-equal sign
The approximately-equal sign ≈ marks an approximation, as in √2 ≈ 1.414. Give a tolerance or precision separately when it matters.
DetailsIdentical-to sign
The identical-to sign ≡ is used for identities and modular congruence. State the convention, and include the modulus for a congruence.
DetailsProportional-to sign
The proportional-to sign ∝ leaves a constant unstated: y ∝ x means y = kx for a fixed k over the range being discussed.
DetailsElement-of sign
The element-of sign ∈ says that an item belongs to a set. Write the item on the left and the set on the right.
DetailsNot-an-element-of sign
The not-an-element-of sign ∉ says that an item is absent from a set. For example, 2 ∉ {1, 3, 5}.
DetailsSubset sign
The subset sign ⊂ compares two sets. Some conventions allow equality; this reference uses it for a proper subset and makes that choice explicit.
DetailsSubset-or-equal sign
The subset-or-equal sign ⊆ says that every element of one set belongs to another. The two sets can be equal.
DetailsUnion sign
The union sign ∪ combines the elements of two sets. An element shared by both sets appears only once in the result.
DetailsIntersection sign
The intersection sign ∩ selects the elements that two sets have in common. It differs from union, which includes elements from either set.
DetailsEmpty-set sign
The empty-set symbol ∅ means a set with no elements. It is neither the number 0 nor the set {0}.
DetailsLogical-and sign
Logical and ∧ is true when both propositions are true. Use it between complete statements, such as P ∧ Q.
DetailsLogical-or sign
Logical or ∨ is usually inclusive: either proposition can be true, and both can be true. An exclusive choice needs a different convention.
DetailsLogical-not sign
Logical not ¬ negates the statement that follows it. Parentheses make the scope clear in a compound expression such as ¬(P ∧ Q).
DetailsTherefore sign
The therefore sign ∴ introduces a conclusion in a mathematical argument. Its three dots form one Unicode character.
DetailsBecause sign
The because sign ∵ introduces a supporting reason in a short derivation. Its dots face the opposite way from the therefore sign ∴.
DetailsPerpendicular sign
The perpendicular sign ⊥ marks a right-angle relationship, as in AB ⊥ CD. Other specialist uses need their own definitions.
DetailsParallel-to sign
The parallel-to sign ∥ relates parallel lines or vectors. It is one character, rather than the two vertical bars in ||.
DetailsAngle sign
The angle sign ∠ labels an angle. In ∠ABC, B is the vertex; add a value and unit when you want to give its measure.
DetailsDegree sign
The degree sign ° follows an angle value, as in 90°, and appears in temperature labels such as °C. It is not a small letter o.
DetailsPrime sign
The prime sign ′ appears in derivatives and measurements. The surrounding notation determines whether it means a derivative, angular minutes, or another unit.
DetailsDouble-prime sign
The double-prime sign ″ is one character. It can mark a second derivative or a measurement such as angular seconds, depending on context.
DetailsMinus sign
The mathematical minus sign − marks subtraction or a negative value. It is distinct from the keyboard hyphen-minus -.
DetailsRatio sign
The ratio sign ∶ compares quantities, as in 2 ∶ 3. It resembles a colon, but the two characters have different code points.
Details