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In mathematical texts, we sometimes shorten "Definition" to "Def." and "Definitions" to "Defs." when used with numbers, e.g.:

According to Defs. 1, 2, and 4, ...

We sometimes use similar abbreviations for Figure (Fig., Figs.), Theorem (Thm., Thms.), Problem (Prob., Probs.), Proposition (Prop., Props.), and Corollary (Cor., Cors.). I believe them to be correct. If you disagree, I'd be eager to hear your arguments. (Assume for simplicity that there are no restrictions from the publisher or no publisher at all.)

I'm still fighting with

  • Exercise, Exercises
  • Example, Examples, and
  • Lemma, Lemmas.

How to abbreviate these six words correctly? (Established abbreviations which may or may not be correct from the viewpoint of the English language are treated in a different question.)

P.S. Please don't ask why we wish to to abbreviate. Just take it for granted. Also assume that the publisher (if present) has no restrictions on this.

  • How is this different from your question at math.SE? Obviously, we can't invent new abbreviations, and there doesn't seem to be an accepted abbreviation for lemma (nor would one seem necessary, since it's only five characters in length!) – P. E. Dant Oct 30 '16 at 20:34
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Not every English word has a well-known or well-accepted abbreviation.

Google is probably your best friend here, just enter "Exercise abbreviation" to see what comes up.

I have seen ex. as an abbreviation for example in more than one text, and ther e is the very well known e.g. which is short for for example.

If you cannot discover a common abbreviation you can invent one, and it would be a good idea to footnote it or otherwise provide a legend indicating what the abbreviation stands for if it's not obvious.

Abbreviating on syllable boundaries is best, keeping in mind that in English, double consonants usually belong to separate syllables. E.g. abbreviate lemma as lem.

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