As far as I know, a proposition is a statement which might be used to prove a theorem but is also of independent interest.
How would you differentiate it from an observation? Would you say it is a proposition with an easy proof?
2026-02-23 06:36:11.1771828571
What is the difference between a proposition and an observation?
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I agree with your characterization of "proposition". I think that by analogy with the physical world an observation in mathematical writing is any statement whose truth is apparent "by inspection". Usually this corresponds to having a short, straightforward proof by an obvious method.
Often the term "observation" it is used more loosely to mean a statement with a proof that the author desires to omit for some other reason. However, this usage has the disadvantage that it may frustrate the reader who does not immediately see why the statement is true.
I think that whether something can be called an observation or not is mostly separate from its role in the paper, unlike the theorem/proposition/lemma distinction. (Of course, a the author should not ask the reader to simply "observe" the truth of the main theorem!)