查看完整版本 : definition of prime

lamhenschel 2014-11-16 01:02 AM

definition of prime

p is a prime⇔
(∀n∈N)(∀q∈N)(1<q<p)[(n|p)⇒(n=1∨n=p∧p≠1∧n∤q)]
Is it correct?

[7] 2014-11-16 06:23 AM

[quote]原帖由 [i]lamhenschel[/i] 於 2014-11-16 01:02 AM 發表 [url=http://www.discuss.com.hk/redirect.php?goto=findpost&pid=402554525&ptid=24030629][img]http://www.discuss.com.hk/images/common/back.gif[/img][/url]
p is a prime⇔
(∀n∈N)(∀q∈N)(1<q<p)[(n|p)⇒(n=1∨n=p∧p≠1∧n∤q)] [/quote]
[img]http://sciencesoft.at/lpng/586c8fd7d3db844257a4137b149a7a912d37fa4.png&size=100*[/img]

[[i] 本帖最後由 [7] 於 2014-11-16 07:18 AM 編輯 [/i]]

lamhenschel 2014-11-16 07:58 AM

p is a prime⇔
(∀n∈N)(∀p∈N)[(n|p)⇒((n=1∨n=p)∧p≠1)]or
p is a prime⇔
(∀n∈N)(∀(p-1)∈N)[(n|p)⇒(n=1∨n=p)]Can we define prime with using existential quantifier?

[[i] 本帖最後由 lamhenschel 於 2014-11-16 09:03 AM 編輯 [/i]]

[7] 2014-11-16 09:02 AM

[quote]原帖由 [i]lamhenschel[/i] 於 2014-11-16 07:58 AM 發表 [url=http://www.discuss.com.hk/redirect.php?goto=findpost&pid=402565930&ptid=24030629][img]http://www.discuss.com.hk/images/common/back.gif[/img][/url]
p is a prime⇔
(∀n∈N)(∀p∈N)[(n|p)⇒((n=1∨n=p)∧p≠1)]or
p is a prime⇔
(∀n∈N)(∀(p-1)∈N)[(n|p)⇒(n=1∨n=p)] [/quote]

[img]http://sciencesoft.at/lpng/586c8fd7d3db844257a4137b149a7a912d37f96.png&size=100*[/img]

[[i] 本帖最後由 [7] 於 2014-11-16 09:30 AM 編輯 [/i]]

lamhenschel 2014-11-16 09:17 AM

p is a prime ⇔(∀n∈N)[(n|p)⇒((n=1⊕n=p)]
p is a prime⇔(∀n∈N)(∀p∈N\{1})[(n|p)⇒(n=1∨n=p)]

[7] 2014-11-16 09:47 AM

[quote]原帖由 [i]lamhenschel[/i] 於 2014-11-16 09:17 AM 發表 [url=http://www.discuss.com.hk/redirect.php?goto=findpost&pid=402569609&ptid=24030629][img]http://www.discuss.com.hk/images/common/back.gif[/img][/url]
p is a prime ⇔(∀n∈N)[(n|p)⇒((n=1⊕n=p)]
p is a prime⇔(∀n∈N)(∀p∈N\{1})[(n|p)⇒(n=1∨n=p)] [/quote]
[img]http://sciencesoft.at/lpng/586c8fd7d3db844257a4137b149a7a912d37f93.png&size=100*[/img]

lamhenschel 2014-11-16 11:52 AM

(∀p∈N\{1})(∀n∈N)(n|p⇒n=1∨n=p)
1|-3 and 3|-3 but -3 is not a prime

[[i] 本帖最後由 lamhenschel 於 2014-11-16 12:19 PM 編輯 [/i]]

[7] 2014-11-16 12:52 PM

[quote]原帖由 [i]lamhenschel[/i] 於 2014-11-16 11:52 AM 發表 [url=http://www.discuss.com.hk/redirect.php?goto=findpost&pid=402577652&ptid=24030629][img]http://www.discuss.com.hk/images/common/back.gif[/img][/url]
(∀p∈N\{1})(∀n∈N)(n|p⇒n=1∨n=p)
1|-3 and 3|-3 but -3 is not a prime [/quote]we r talking only natural number, i.e. p not=1 just now means p in N\{1}. U use p in N\{1} in replace of p not=1 for a politically correct statment la.



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[7] 2014-11-16 01:22 PM

[quote]原帖由 [i]lamhenschel[/i] 於 2014-11-16 11:52 AM 發表 [url=http://www.discuss.com.hk/redirect.php?goto=findpost&pid=402577652&ptid=24030629][img]http://www.discuss.com.hk/images/common/back.gif[/img][/url]
(∀p∈N\{1})(∀n∈N)(n|p⇒n=1∨n=p)
1|-3 and 3|-3 but -3 is not a prime [/quote]
Also, not "for all" p, u r talking to define p, no need to qualify it.



[url=http://m.discuss.com.hk][img=100,23]http://n2.hk/d/images/r10/mobile.jpg[/img][/url]

[7] 2014-11-16 01:25 PM

[quote]原帖由 [i]lamhenschel[/i] 於 2014-11-16 11:52 AM 發表 [url=http://www.discuss.com.hk/redirect.php?goto=findpost&pid=402577652&ptid=24030629][img]http://www.discuss.com.hk/images/common/back.gif[/img][/url]
(∀p∈N\{1})(∀n∈N)(n|p⇒n=1∨n=p)
1|-3 and 3|-3 but -3 is not a prime [/quote]we r talking only natural number, i.e. p not=1 just now means p in N\{1}. U use p in N\{1} in replace of p not=1 for a politically correct statment la.



[url=http://m.discuss.com.hk][img=100,23]http://n2.hk/d/images/r10/mobile.jpg[/img][/url]
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查看完整版本: definition of prime