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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:
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 font used in the TeX rendering is an italic style. This is in line with the convention that variables should be italicized. As Greek letters are more often than not used as variables in mathematical formulas, a Greek letter appearing similar to the TeX rendering is more likely to be encountered in works involving mathematics.
The English-language titles of compositions (books and other print works, songs and other audio works, films and other visual media works, paintings and other artworks, etc.) are given in title case, in which every word is given an initial capital except for certain less important words (as detailed at Wikipedia:Manual of Style/Capital letters ...
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 ...
All Mathematics is Symbolic Logic. [8] Bertrand Russell 1903. Peirce did not think that mathematics is the same as logic, since he thought mathematics makes only hypothetical assertions, not categorical ones. [11] Russell's definition, on the other hand, expresses the logicist view without reservation. [9]
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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