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434:, it is grammatically correct, but semantically confusing. In mathematics, one must always take care when words have a mathematical meaning that differ from their common (usual) meaning. In the case of "common divisor", "common" refers to "common to two integers". In "commonly divisible", "commonly" is not used in its common meaning, but is used in place of "simultaneously divisible". So the formulation is confusing. By the way Khan Academy is not a reliable source for attesting a common use of "commonly divisible"
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divisor" uses the second meaning of the adjective "common", and the phrase "commonly divisible" uses the corresponding adverbial form. Anyone who understands the phrase "greatest common divisor" should, by applying standard rules of
English, be able to convert it to the corresponding adverbial form, and vice-versa.
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The most common meaning of "common" is probably "widespread; public". The second-most common meaning of "common" is "shared; joint". Both of these can be turned into an adverb: "commonly" meaning "frequently; often; usually" and "commonly" meaning "in common; jointly". The phrase "greatest common
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The lead can be difficult for someone first coming to this concept, even though the concept is not complicated. I suggest that a sentence like the one Dan
Harkless suggested be used, but with changes to avoid objections about 'coprime' not being a noon. Another clarification would be to expand on
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P.S. I feel like it is strangely common (at least, this is not the first time) for you, a PhD mathematician who writes
English well but not fluently, to lecture me, a PhD mathematician who writes English fluently, on basic points of English grammar and its use in mathematics. I promise that I will
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This depends on the probability law that is chosen, and, except for the case 4 (setwise coprimality), it should be an exercise of probability theory to deduce the probability from the case of the probability of pairwise coprimality. In any case, per
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Example: 6, 10, 15; 6 and 10 are both divisible by 2, 6 and 15 are both divisible by 3, 10 and 15 are both divisible by 5, but the greatest common divisor of 6, 10, and 15 is 1.
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When three different random integers are selected, there are five different cases of the three numbers having a common divisor or being coprime to one another:
360:"...As specific examples, 14 and 25 are coprime, being commonly divisible only by 1, while 14 and 21 are not coprime, because they are both divisible by 7..."
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By chance, I read that a few days ago and found it perfectly understandable. The "proposed" version is also ok. commonly divisible seems to be used: see (
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2. Exactly one pair of the three integers have a common divisor greater than 1 and the other integer is relatively prime to both the other two integers.
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4. All three pairs of the three integers have a common divisor greater than 1 but the greatest common divisor of all three numbers is 1.
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Indeed, that's because it's a completely standard
English language construction -- there's nothing jargony or obscure at all about it. --
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Huh?!?! If you're trying to say that "14 and 25 are coprime, sharing no factors in common between them except 1," then for God's sake,
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3. Exactly two pairs of the three integers have a common divisor greater than 1 and one pair of integers is relatively prime.
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This article is or was the subject of a Wiki
Education Foundation-supported course assignment. Further details are available
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Example: 4, 6, 9; 4 and 6 are both divisible by 2, 6 and 9 are both divisible by 3, and 4 and 9 are relatively prime.
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390:, I agree. "Commonly divisible" is not a common phrase for saying "having a common divisor". I have fixed it.
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Well. It may not be my recommended wording, but at least it's a lot clearer than it was! Thanks. 😊
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What is the probability that each of the five cases will occur when choosing three random integers?
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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To be clear: this is just forum-y chatting, I am not trying to get anyone to change the article.
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Example: 3, 4, 10; 4 and 10 are divisible by 2, 3 is relatively prime to both 4 and 10.
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5. No two integers have a common divisor greater than 1 (pairwise coprime).
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Example: 3, 4, 5; 3, 4, and 5 are all relatively prime to one another.
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never attempt to lecture you on fine points of French usage or grammar!
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the example of 8 and 9 by naming the prime factors of each (2 and 3).
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1. All three integers have a common divisor greater than 1.
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Example: 4, 6, 8; 4, 6, and 8 are all divisible by 2.
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