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I am writing a scientific paper. I have made several assumptions which are properly ordered. When I cite them, shall I use, i.e., "... by the Assumption 1,..." or simply "... by Assumption 1,..."?

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As a side point, you shouldn't capitalize "assumption" in the phrases you quoted. – JSBձոգչ Dec 30 '10 at 23:01
Oh and it seems you misused "i.e.". It stands for "id est", which is Latin for "that is", and it introduces an explanation or specification. Use "e.g." to introduce examples: it stands for "exempli gratia", which means "for the sake of example". – Cerberus Dec 31 '10 at 1:15
@JSBangs: I disagree. It depends. If, for instance, one has a numbered list of "Assumptions" in bold, it is conventional in scientific papers to capitalize and write "by Assumption 1", just as one would write "by Theorem 1", "by Corollary 1" or "by Definition 1", "by Claim 1", etc. – ShreevatsaR Dec 31 '10 at 4:38
Thanks very one. Your comments are very helpful. Thanks Cerberus, I should use "e.g." instead of "i.e.". :-) – Anand Dec 31 '10 at 9:52
up vote 1 down vote accepted

It's not necessary to use the article "the" in the case you specify.

You would say "Assumption #2 is ..."

If you want to use the definitive article, preface with the ordinal number:

"The second assumption presumes that..."

From Wikipedia:

A definite article indicates that its noun is a particular one (or ones) identifiable to the listener. It may be the same thing that the speaker has already mentioned, or it may be something uniquely specified. The definite article in English is the.

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Thank you very much. I am clear now.:-) – Anand Dec 31 '10 at 9:53

You should use "by Assumption 1". (Not "by the Assumption 1", "by Assumption #1", "by assumption 1", etc.)

This is the convention in scientific papers — it exactly parallels the way you would write, for instance, "by Theorem 3", "by Definition 2", "by Corollary 1", "by Lemma 3", "by Claim 4", etc., and not "by the Theorem 3" or "by the second definition" or other forms, even if some of them may be grammatically correct too.

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Thanks ShreevatsaR. I must choose one answer between yours and Morganpdx's. Since his is just a little earlier than you. I choose his. Yours is also very helpful, actually they are the same. :-) Thank you! – Anand Dec 31 '10 at 9:55
@Anand: Glad it helped. But let me just point out that they are not the same: neither of his suggestions — "Assumption #2" and "the second assumption" – is what you should normally use in your context, though if the only message you're taking is that you shouldn't use "the", then it's fine. – ShreevatsaR Dec 31 '10 at 10:07

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