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May 1st, 2015, 10:21 PM   #1
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factorial meaning

Hello,

I'm not sure if this is a good Critical thinking question but here goes

What is the mathematical meaning of factorial? (besides its mathematical definition, n! = nx(n-1)x(n-2)....x2x1)

Thanks,
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May 2nd, 2015, 02:13 AM   #2
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It has no meaning other than that contained in its definition, the factorial of a positive integer is defined to be the product of all the positive integers less than or equal to it.

CB

Last edited by skipjack; May 2nd, 2015 at 02:53 PM.
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May 2nd, 2015, 02:53 AM   #3
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Wikipedia tells me: "there are n! ways to arrange n distinct objects into a sequence"...
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May 2nd, 2015, 05:57 AM   #4
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Quote:
Originally Posted by ofransen View Post
Wikipedia tells me: "there are n! ways to arrange n distinct objects into a sequence"...
That's one application of the factorial. I wouldn't call it the "meaning".
In general, mathematical "objects" do not have a "meaning" other than their definition. That's the reason mathematics is so "flexible"- you can assign a meaning for a particular application. In that sense "there are n! ways to arrange n distinct objects into a sequence" is a meaning assigned to the factorial for that particular application.
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May 2nd, 2015, 01:41 PM   #5
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Thank you very much.
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May 2nd, 2015, 11:50 PM   #6
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Yes, I know, but I wasn't sure what you meant by "meaning". What is the meaning of cosine for example?
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