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There are several issues of writing style that are particularly relevant in mathematical writing. In the interest of clarity, sentences should not begin with a symbol. Do not write: Suppose that G is a group. G can be decomposed into cosets, as follows. Let H be the corresponding subgroup of G. H is then finite. Instead, write something like:
Definition There should be an exact definition, in mathematical terms; often in a Definition(s) section, for example: Let S and T be topological spaces, and let f be a function from S to T. Then f is called continuous if, for every open set O in T, the preimage f −1 (O) is an open set in S. Examples
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
The rationale behind this is that it enables design and usage of special mathematical characters that include all necessary properties to differentiate from other alphanumerics, e.g. in mathematics an italic "𝐴" can have a different meaning from a roman letter "A".
The words 1, r, r 2, ..., r n-1, s, sr, ..., sr n-1 are a normal form for the dihedral group Dih n with S = {s, r} and 1 as above. The set of words of the form x m y n for m,n ∈ Z are a normal form for the direct product of the cyclic groups x and y with S = {x, y}. The set of reduced words in S are the unique normal form for the free group ...
In applied fields the word "tight" is often used with the same meaning. [2] smooth Smoothness is a concept which mathematics has endowed with many meanings, from simple differentiability to infinite differentiability to analyticity, and still others which are more complicated. Each such usage attempts to invoke the physically intuitive notion ...
The style is most commonly used to represent the number sets (natural numbers), , (rational numbers), (real numbers), and (complex numbers). To imitate a bold typeface on a typewriter , a character can be typed over itself (called double-striking ); [ 1 ] symbols thus produced are called double-struck , and this name is sometimes adopted for ...
In LaTeX text mode the math method above is inappropriate, as letters will be in math italic, so the command n\textsuperscript{th} will give n th and A\textsubscript{base} will give A base (textual subscripts are rare, so \textsubscript is not built-in, but requires the fixltx2e package). As in other systems, when using UTF-8 encoding, the ...