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3.10.3 Letters and Letter-like Forms

Greek Letters

The complete collection of Greek letters in Mathematica.

You can use Greek letters as the names of symbols. The only Greek letter with a built-in meaning in StandardForm is , which Mathematica takes to stand for the symbol Pi.

Note that even though on its own is assigned a built-in meaning, combinations such as or have no built-in meanings.

The Greek letters and look very much like the operators for sum and product. But as discussed above, these operators are different characters, entered as \[Sum] and \[Product] respectively.

Similarly, is different from the operator \[Element], and is different from or \[Micro].

Some capital Greek letters such as \[CapitalAlpha] look essentially the same as capital English letters. Mathematica however treats them as different characters, and in TraditionalForm it uses \[CapitalBeta], for example, to denote the built-in function Beta.

Following common convention, lower-case Greek letters are rendered slightly slanted in the standard fonts provided with Mathematica, while capital Greek letters are unslanted.

Almost all Greek letters that do not look similar to English letters are widely used in science and mathematics. The capital xi is rare, though it is used to denote the cascade hyperon particles, the grand canonical partition function and regular language complexity. The capital upsilon is also rare, though it is used to denote particles, as well as the vernal equinox.

Curly Greek letters are often assumed to have different meanings from their ordinary counterparts. Indeed, in pure mathematics a single formula can sometimes contain both curly and ordinary forms of a particular letter. The curly pi is rare, except in astronomy.

The final sigma is used for sigmas that appear at the ends of words in written Greek; it is not commonly used in technical notation.

The digamma , koppa , stigma and sampi are archaic Greek letters. These letters provide a convenient extension to the usual set of Greek letters. They are sometimes needed in making correspondences with English letters. The digamma corresponds to an English w, and koppa to an English q. Digamma is occasionally used to denote the digamma function PolyGamma[x].

Variants of English Letters

Some commonly used variants of English letters.

By using menu items in the notebook front end, or explicit StyleBox objects, you can make changes in the font and style of ordinary text. However, such changes are usually discarded whenever you send input to the Mathematica kernel.

Script, gothic and double-struck characters are however treated as fundamentally different from their ordinary forms. This means that even though a C that is italic or a different size will be considered equivalent to an ordinary C when fed to the kernel, a double-struck will not.

Different styles and sizes of C are treated as the same by the kernel. But gothic and double-struck characters are treated as different.

In[1]:=

Out[1]=

In standard mathematical notation, capital script and gothic letters are sometimes used interchangeably. The double-struck letters, sometimes called blackboard or openface letters, are conventionally used to denote specific sets. Thus, for example, conventionally denotes the set of complex numbers, and the set of integers.

Dotless i and j are not usually taken to be different in meaning from ordinary i and j; they are simply used when overscripts are being placed on the ordinary characters.

\[WeierstrassP] is a notation specifically used for the Weierstrass P function WeierstrassP.

Complete alphabets of variant English letters.

Hebrew Letters

Hebrew characters.

Hebrew characters are used in mathematics in the theory of transfinite sets; is for example used to denote the total number of integers.

Units and Letter-like Mathematical Symbols

Units and letter-like mathematical symbols.

Mathematica treats or \[Degree] as the symbol Degree, so that, for example, 30 is equivalent to 30 Degree.

Note that , and are all distinct from the ordinary letters (\[Mu]), (\[CapitalARing]) and (\[CapitalOSlash]).

Mathematica interprets as Infinity, as E, and both and as I. The characters , and are provided as alternatives to the usual upper-case letters E and I.

and are not by default assigned meanings in StandardForm. You can therefore use to represent a pi that will not automatically be treated as Pi. In TraditionalForm is interpreted as EulerGamma.

Operators that look like letters.

is an operator while , and are ordinary symbols.

In[1]:= {Del f, HBar^2, 45°, 5000¥} // FullForm

Out[1]//FullForm=

Shapes, Icons and Geometrical Constructs

Shapes.

Shapes are most often used as "dingbats" to emphasize pieces of text. But Mathematica treats them as letter-like forms, and also allows them to appear in the names of symbols.

In addition to shapes such as \[EmptySquare], there are characters such as \[Square] which are treated by Mathematica as operators rather than letter-like forms.

Icons.

You can use icon characters just like any other letter-like forms.

In[1]:= Expand[(HappySmiley + Wolf)^4]

Out[1]=

Notation for geometrical constructs.

Since Mathematica treats characters like as letter-like forms, constructs like BC are treated in Mathematica as single symbols.

Textual Elements

Characters used for punctuation and annotation.

Other characters used in text.

Characters used in building sequences and arrays.

The under and over braces grow to enclose the whole expression.

In[1]:= Underoverscript[Expand[(1 + x)^4],
\[UnderBrace], \[OverBrace]]

Out[1]=

Extended Latin Letters

Mathematica supports all the characters commonly used in Western European languages based on Latin scripts.

Variants of English letters.

Most of the characters shown are formed by adding diacritical marks to ordinary English letters. Exceptions include \[SZ] , used in German, and \[Thorn] and \[Eth] , used primarily in Old English.

You can make additional characters by explicitly adding diacritical marks yourself.

Adding marks above and below characters.

Diacritical marks to add to characters.