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Is number Z even? (1) Z!=1 (2) |Z|!=Z

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stolyar
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Is number Z even? (1) Z!=1 (2) |Z|!=Z [#permalink] New post   14 Jun 2004, 12:06
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Is number Z even?

(1) Z!=1

(2) |Z|!=Z



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Re: Is number Z even? (1) Z!=1 (2) |Z|!=Z [#permalink] New post   14 Jun 2004, 12:50
Yep, C it is.

With statement 1, Z could be 0 or 1

With statement 2, Z could be 2 or 1

Z = 1 and 1 is odd.
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Re: Is number Z even? (1) Z!=1 (2) |Z|!=Z [#permalink] New post   17 Jun 2004, 16:15
I don't really understand why 0!=1?
I understand 3! will be 3×2×1=6, but I don't know
how to calculate 0! Please let me know. Thank you.
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Re: Is number Z even? (1) Z!=1 (2) |Z|!=Z [#permalink] New post   18 Jun 2004, 01:53
TIANMU wrote:
I don't really understand why 0!=1?
I understand 3! will be 3×2×1=6, but I don't know
how to calculate 0! Please let me know. Thank you.


Don't worry, 0! = 1 BY DEFINITION. Had you known definition of gamma-function, you would have come with such property: gamma(n) = (n-1)!, gamma(1) = 1. => 0! = 1.

how is gamma function defined? It is equal to (see picture):
Attachments

gamma.doc [15.5 KiB]
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mba
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Re: Is number Z even? (1) Z!=1 (2) |Z|!=Z [#permalink] New post   18 Jun 2004, 07:34
I believe (B) should be the answer, because |Z|! will be Z only when Z is -1 or 1. Hence Z is ODD. Any explanations??
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Re: Is number Z even? (1) Z!=1 (2) |Z|!=Z [#permalink] New post   18 Jun 2004, 07:56
mba wrote:
I believe (B) should be the answer, because |Z|! will be Z only when Z is -1 or 1. Hence Z is ODD. Any explanations??


-1 does not satisfy the second equation, for any factorial is always POSITIVE.
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Re: Is number Z even? (1) Z!=1 (2) |Z|!=Z [#permalink] New post   18 Jun 2004, 08:35
Emmanuel wrote:
TIANMU wrote:
I don't really understand why 0!=1?
I understand 3! will be 3×2×1=6, but I don't know
how to calculate 0! Please let me know. Thank you.


Don't worry, 0! = 1 BY DEFINITION. Had you known definition of gamma-function, you would have come with such property: gamma(n) = (n-1)!, gamma(1) = 1. => 0! = 1.

how is gamma function defined? It is equal to (see picture):


Thank you very much, Emmanuel !
I didn't know this definition, but I learn it now.



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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Re: Is number Z even? (1) Z!=1 (2) |Z|!=Z [#permalink]
18 Jun 2004, 08:35
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