A symbol should not be used in the statement of a theorem (or in its proof exactly once. If it is useful to have a name for an arbitrary bijective function in the proof (as it probably will be), then "f" can be introduced there. 8. Explain the meaning of every symbol that you introduce Although what you intended may seem clear, don't assume this. For 2k and k has never appeared before, then say example, if you write n that k is an integer (if indeed k is an integer) 9. se "frozen symbols" properly. If m and n are typically used for integers (as they probably are), then don't use them for real numbers. If A and Bare used for sets, then don't use these as typical elements of a set. If f is used for a function, then don't use this as an integer. Write symbols that the reader would expect. To do otherwise could very well confuse the reader. 10. Use consistent symbols. Unless there is some special reason to the contrary, use symbols that "fit together. Otherwise, it is distracting to the reader. Instead of writing: and y 2r for some integers a and r replace 2r by 2b (where then, of course, we write "for some integers a and b". On the other hand, you might prefer to write x 2r and y 2s