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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:
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 ...
Equivalence class: given an equivalence relation, [] often denotes the equivalence class of the element x. 3. Integral part : if x is a real number , [ x ] {\displaystyle [x]} often denotes the integral part or truncation of x , that is, the integer obtained by removing all digits after the decimal mark .
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 ...
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".
def – define or definition. deg – degree of a polynomial, or other recursively-defined objects such as well-formed formulas. (Also written as ∂.) del – del, a differential operator. (Also written as.) det – determinant of a matrix or linear transformation. DFT – discrete Fourier transform.
The consequence of these features is that a mathematical text is generally not understandable without some prerequisite knowledge. For example, the sentence "a free module is a module that has a basis" is perfectly correct, although it appears only as a grammatically correct nonsense, when one does not know the definitions of basis, module, and free module.
In literature, writing style is the manner of expressing thought in language characteristic of an individual, period, school, or nation. [1] As Bryan Ray notes, however, style is a broader concern, one that can describe "readers' relationships with, texts, the grammatical choices writers make, the importance of adhering to norms in certain contexts and deviating from them in others, the ...