Technical Reports

Operators

For relation symbols, the choice of a vertical or forward-slanting stroke typically seems to be an aesthetic one, but both slants might appear in a given context. However, a back-slanted stroke almost always has a distinct meaning compared to the forward-slanted stroke. See Section 2.18, Variation Selector for more information on some particular variants.

The operator U+2208 ∈ ELEMENT OF is occasionally rendered with a taller shape than shown in the code charts. Mathematical handbooks and standards treat these characters as variants of the same glyph. U+220A ∊ SMALL ELEMENT OF is a distinctively small version of the element of that originates in mathematical pi fonts. (Its glyph should be upright, not slanted).

The operators U+226B ≫ MUCH GREATER-THAN and U+226A ≪ MUCH LESS-THAN are sometimes rendered in a nested shape, but the Unicode Standard provides a single encoding for each operator.

A large class of unifications applies to variants of relation symbols involving equality, similarity, and/or negation. Variants involving one- or two-barred equal signs, one- or two-tilde similarity signs, and vertical or slanted negation slashes and negation slashes of different lengths are not separately encoded. Thus, for example, U+2288 ⊈ NEITHER A SUBSET OF NOR EQUAL TO, is the archetype for at least six different glyph variants noted in various collections.

In a few exceptional instances, essentially stylistic variants are separately encoded because the need for round trip character mapping to other standards that distinguish the two forms. Examples include U+2265 ≥ GREATER-THAN OR EQUAL TO, which is distinguished from U+2267 ≧ GREATER-THAN OVER EQUAL TO; the same distinction applies to U+2264 ≤ LESS-THAN OR EQUAL TO and U+2266 ≦ LESS-THAN OVER EQUAL TO. 

Greek-Derived Operators. Several mathematical operators derived from Greek characters have been given separate encodings because they are used differently than the corresponding letters. These operators may occasionally occur in context with Greek-letter variables. They include U+2206 ∆ INCREMENT, U+220F ∏ N-ARY PRODUCT, and U+2211 ∑ N-ARY SUMMATION. The latter two are large operators that take limits. Some typographical aspects of operators are discussed in Section 3.2, Classification by Typographical Behavior. For example, the n-ary operators are distinguished from letter variables by their larger size and the fact that they take limit expressions.

Minus sign. U+2212 − MINUS SIGN is the preferred representation of the unary and binary minus sign rather than the ASCII-derived U+002D - HYPHEN-MINUS, because minus sign is unambiguous and because it is rendered with a more desirable length, usually longer than a hyphen.

Miscellaneous Symbols.  The symbol U+2205 ∅ EMPTY SET is distinct from the letters Ø (U+00D8) and ø (U+00F8), even though it’s historically derived from the letter forms. A widespread alternate symbol for the empty set is a slashed digit zero. This can be encoded as U+0030 DIGIT ZERO followed by U+0338 COMBINING LONG SOLIDUS OVERLAY.

The range from U+22EE ⋮ to  U+22F1 ⋱ contains a set of ellipses used in matrix notation.

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