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 2008-08-29, 12:53 #45 Housemouse     Feb 2008 25 Posts Do these functions have an infinite number of values but a specific number of prime values? Last fiddled with by Housemouse on 2008-08-29 at 12:54
2008-08-29, 13:10   #46
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 Originally Posted by Housemouse Do these functions have an infinite number of values but a specific number of prime values?

Go look up the definition of 'domain' and 'range' in the context of
studying functions.

 2008-08-29, 13:13 #47 Wacky     Jun 2003 The Texas Hill Country 44116 Posts At this point, I will join Dr. Silverman and suggest that you study the elementary mathematics related to the definitions and properties of the terms that you are attempting to use. With some more of that understanding, you might realize how your question is just ridiculous. Suggested topics: Domain, range, mapping, function (Bob: Sorry, I didn't realize that you were formulating the same sort of reply) Last fiddled with by Wacky on 2008-08-29 at 13:15 Reason: Dr. Silverman beat me to the reply
 2008-08-29, 13:27 #48 Housemouse     Feb 2008 25 Posts Wacky Can you please give me an example of one function that has an infinate number of values, but can be proven to have exactly 10 prime values?
2008-08-29, 13:37   #49
R.D. Silverman

Nov 2003

11101001001002 Posts

Quote:
 Originally Posted by Housemouse Can you please give me an example of one function that has an infinate number of values, but can be proven to have exactly 10 prime values?
f(x) = x, for x = 2,3,5,7,11,13,17,19,23,29
= x^2 for all other x.

2008-08-29, 13:38   #50
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

17EB16 Posts

Quote:
 Originally Posted by Housemouse Can you please give me an example of one function that has an infinate number of values, but can be proven to have exactly 10 prime values?
Perhaps: f(x)=29-x^2 ?

Last fiddled with by retina on 2008-08-29 at 14:16

2008-08-29, 13:39   #51
xilman
Bamboozled!

"πΊππ·π·π­"
May 2003
Down not across

246308 Posts

Quote:
 Originally Posted by Housemouse Can you please give me an example of one function that has an infinate number of values, but can be proven to have exactly 10 prime values?
I can.

Let f(x) be the function such that f(x) = x for 1<=x<=29 and f(x) = 4x for all all other values of x.

Paul

Last fiddled with by xilman on 2008-08-29 at 14:07 Reason: Add spoiler tags

 2008-08-29, 13:43 #52 Wacky     Jun 2003 The Texas Hill Country 32·112 Posts Housemouse, Yes, I can. However I choose to not do so because, as noted previously, it is trivial. If, instead, you will show that you have done the "homework" that I have suggested, and still cannot formulate such a function, I will be happy to continue the discussion.
2008-08-29, 13:52   #53
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by retina Perhaps: y=29-x^2 ?
No.

2008-08-29, 14:17   #54
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

17EB16 Posts

Quote:
 Originally Posted by R.D. Silverman No.
f(x)=29-x^2 ?

2008-08-29, 14:24   #55
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by retina f(x)=29-x^2 ?
Although not explicitly stated, I believe that the domain is N. Now,
f(x) is prime for x = 0, 4 and no other. If you accept the more general
definition of prime (i.e. not restricted to just N) then f(x) will be prime
i.o. (although a proof is lacking). If we allow x \in R, then f(x) is
indeed prime the required number of times.

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