However, convincing the reader of the simple truth of your work is not sufficient. One technique to assist you in revealing the complex logical structure of your paper is a proper naming of results. Use I only for something specific to yourself. The purpose of this paper is to provide assistance for young mathematicians writing their first paper. If you do mathematics purely for your own pleasure, then there is no reason to write about it.
A small reason is the hope that what I said isn't quite right; and, anyway, I'd like a chance to try to do what perhaps cannot be done. If you insist on starting the sentence with a mention of the thing the symbol denotes, put the appropriate word in apposition, thus: "The set X belongs to the class C, This is your first goal in mathematical writing. Halmos, Menahem M. Proofs such as Godel's proof of undecidability?
The way to make the human reader's task less demanding is obvious: write the proof forward. As for "if On the contrary, most proofs could be modeled with very complicated graphs, in which several basic hypotheses combine with a few well known theorems in a complex way. A well-worded theorem will make writing the proof much easier. Thus, one activity of the active mathematical reader is to note the places at which a sample of written mathematics becomes unclear, and to avoid making the same mistakes his own writing.
The rules for writing a book apply, with minor modification, to writing a research paper, or to preparing a lecture. Quotes The sentences are rephrased by myself.
If you need eight conditions and five conclusions, you'll probably need a term for that. One technique to assist you in revealing the complex logical structure of your paper is a proper naming of results. Replace it by "each" or "every", or recast the whole sentence" p. Gordon told me this. One reason is that it is concerned with the kind of activity that mathematicians engage in when they prove things. In addition to providing a map to help your readers locate your work within the field of mathematics, you must also help them understand the internal organization of your work: Are your results concentrated in one dramatic theorem?
It must communicate something of the substances to the experts in your field as well as to the novices who will be interested. A statement of a theorem should be just that, self-contained, no chit-chat, no superfluous hypotheses and of course no missing hypotheses. Does is connect two previously unrelated aspects of mathematics? Which ones follow naturally from others, and which ones are the real work horses of the paper?
Experience has shown, however, that this is a wild-goose chase.