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The proofs will all be based on the following remark

Is the “remark” used rightly?

“Remark” was translated into a Chinese word with the meaning of "fact".

It seems “remark” has the meaning of critique, converse and observation.

So which one is proper?

  • It is not bad if you clarify more exactly what you ask. Do you ask two questions: one either in the original text the word "remark" is used correctly, and secondly what is the meaning of "remark" in the context? – Theta30 Sep 6 '13 at 16:18
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Since the quoted fragment contains the word "proof", it is likely to come from a scientific text. It is common in the scientific literature to use the word remark in the sense of observation, comment. It is something you mention without much detail, hence it is less than, say, a proposition or law. By "less" I mean in terms of complexity, not in terms of soundness or usefulness; a remark can be, as suggested by your text, very handy. So yes, that text is correct.

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In a scienctific context, you wouldn't want to base a proof on a remark. As Theta30 says, a remark is an incidental obeservation or comment.

You might consider the word axiom, meaning a fact that is accepted without proof (usually because its obviously true, in the context where it is used), and used as the basis to prove further claims.

Or theorem, meaning a proposition whose proof must be established. Once a theorem has been proved, it may be used as the basis for proving other theorems.

  • No, it's fine to base a proof on a remark. It may or may not be appropriate in the OP's situtation, we can't know without more context. – Gilles 'SO- stop being evil' Sep 17 '13 at 11:30
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Instead of the word "remark", we can use the word "evidence" or "gospel" so the correct meaning of the sentence is derived.

The word "remark" can be used but it is not the actual word that derives the correct meaning of the sentence.

  • This the sentence mentions a proof, this is from a scientific or philosophical text. Remark can be correct in a scientific context. Gospel is right out; evidence would be hard to justify. – Gilles 'SO- stop being evil' Sep 17 '13 at 11:29

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