Mathematical operator entities: sets, logic and calculus
The entity reference tool carries the common operators of set theory, logic and calculus, each with a named reference. This page lists them with their code points and the traps in using them.
At a glance
- Character
- ∑ ∏ ∫ ∂ ∇ ∈ ∪ ∩ ⊂ ∀ ∃ ∅ ∧ ∨ ¬ ∴ ≡
- Named entity
- ∑ ∏ ∫ ∂ ∇ ∈ ∪ ∩ ⊂ ∀ ∃ ∅ ∧ ∨ ¬ ∴ ≡
- Decimal reference
- ∑ ∏ ∫ ∂ ∇ ∈ ∪ ∩ ⊂ ∀ ∃ ∅ ∧ ∨ ¬ ∴ ≡
- Hex reference
- ∑ ∏ ∫ ∂ ∇ ∈ ∪ ∩ ⊂ ∀ ∃ ∅ ∧ ∨ ¬ ∴ ≡
- Unicode code point
- U+2211, U+220F, U+222B, U+2202, U+2207, U+2208 and neighbours
- Unicode name
- N-ARY SUMMATION, N-ARY PRODUCT, INTEGRAL, PARTIAL DIFFERENTIAL, NABLA, ELEMENT OF and the set and logic operators
- In the entity reference
- Math
In detail
The large operators, summation, product and integral, are drawn at a size meant to carry limits above and below them. Written as bare characters in running text they get no limits at all, so a sum over an index has to state its range in words or in adjacent subscript markup. That is acceptable in a sentence mentioning a formula and inadequate for presenting one.
Set membership and its relatives are the entities most often mistyped, because the names are abbreviations rather than words. Membership is ∈ from is in, union is ∪ and intersection is ∩ from the cup and cap shapes, subset is ⊂ and superset is ⊃. That last one collides in the mind with the superscript entities, and writing ⊃ when you meant ² produces a set symbol in the middle of a unit.
The summation sign is not the Greek capital sigma, even though the two look alike in most fonts. Summation is U+2211 and the Greek letter is U+03A3, and the same split exists between the product sign at U+220F and the Greek capital pi. A search index that normalises will not merge them, so a formula stored with the Greek letter will not match a search for the operator.
For anything a reader has to follow, MathML is the right output and these characters are the wrong one. MathML positions limits, scales the operator to its content and exposes the structure to assistive technology, none of which a run of characters can do. Keep the entities for a symbol mentioned in a sentence, a legend, or a table header.
Examples
<p>If x ∈ A ∩ B then x ∈ A and x ∈ B.</p>
<p>A ⊂ B, and A ∪ B = B.</p>
<p>The empty set is written ∅.</p><p>summation operator: ∑ (U+2211)</p>
<p>Greek capital sigma: Σ (U+03A3)</p>
<p>product operator: ∏ (U+220F)</p>
<p>Greek capital pi: Π (U+03A0)</p>Things that catch people out
- ⊃ is the superset relation and ² is a superscript two. One letter apart, and a unit written with the wrong one becomes a set expression.
- Substituting a Greek capital sigma for the summation operator looks identical and breaks any search, comparison or conversion that goes through the code point.
- Large operators drawn as plain characters cannot carry limits. A sum without a stated range is not a formula, it is a decoration.
Try it: HTML Entity Reference
Search 152 entities across 9 categories, switch the copy format between the character, the name, the decimal form and the hex form, and copy in one click.
HTML Entity Reference
LOCAL · Browser-OnlySearchable reference of 150+ HTML entities with one-click copy in any format
152 entities across 9 categories
Commonly Used
→Arrows(13)
±Math(35)
$Currency(8)
…Punctuation(21)
©Symbols(24)
πGreek(30)
½Fractions(6)
●Geometric(7)
æLatin Special(8)
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Related HTML entities
All html entities →Square root symbol (√) in HTML
The radical sign at U+221A, its entity forms, why it has no overbar, when parentheses are compulsory, and the cube and fourth root characters.
Not equal to sign (≠) in HTML
The not equal to sign at U+2260, its entity forms, why the composed and combining versions differ, and how it compares to the operators used in code.
Sigma (σ) in HTML
The Greek letter sigma at U+03A3 and U+03C3, its entity forms, the summation operator it is confused with, and the final sigma used at the end of a word.
Right arrow (→) in HTML
The rightwards arrow at U+2192, its entity forms, using it in a call to action without confusing a screen reader, and how it behaves in right to left text.
Left arrow (←) in HTML
The leftwards arrow at U+2190, its entity forms, why a back link needs a real destination, and the direction problem in right to left interfaces.
Up and down arrows (↑ and ↓) in HTML
The upwards and downwards arrows at U+2191 and U+2193, their entity forms, their use as sort indicators, and why aria-sort does the real work.
Tools for this
- HTML Entity Reference Free online HTML entity reference - search and copy HTML entities with live preview
- Unicode Character Finder Free online unicode character finder - search and copy special Unicode characters and symbols