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 Post subject: About a function over natural numbers which does not exist.Posted: Mon, 28 Nov 2011 05:33:53 UTC
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Joined: Mon, 14 Feb 2011 22:39:36 UTC
Posts: 73
Location: Chile
Show that is not there a function such that

Proof: (For )

It easy view:

1 for all .

By induction it is proved that for all ,

For It is trivial, If this is true for then:

As would be for ?

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 Post subject: Re: About a function over natural numbers which does not exiPosted: Mon, 28 Nov 2011 05:38:15 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12098
Location: Austin, TX
eraldcoil wrote:
Show that is not there a function such that

Proof: (For )

It easy view:

1 for all .

By induction it is proved that for all ,

For It is trivial, If this is true for then:

As would be for ?

What? the way you've written it you want , why not just write that? And presumably you want and not the square of , otherwise it's trivial. In any case, clarify your function definition, it seems based on what you've written that you want just , which I sincerely doubt is the case, since you can just let be the (functional) square of the successor function if so.

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 Post subject: Re: About a function over natural numbers which does not exiPosted: Mon, 28 Nov 2011 13:36:43 UTC
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Joined: Thu, 7 Apr 2005 16:32:15 UTC
Posts: 1276
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eraldcoil wrote:
Show that is not there a function such that

Proof: (For )

It easy view:

1 for all .

By induction it is proved that for all ,

For It is trivial, If this is true for then:

As would be for ?

What? the way you've written it you want , why not just write that? And presumably you want and not the square of , otherwise it's trivial. In any case, clarify your function definition, it seems based on what you've written that you want just , which I sincerely doubt is the case, since you can just let be the (functional) square of the successor function if so.

functional square of the successor function is a fancy way of saying
f(n)=n+2 which has
f(f(n))=f(n+2)=(n+2)+2=n+4

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 Post subject: Re: About a function over natural numbers which does not exiPosted: Mon, 28 Nov 2011 18:15:38 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12098
Location: Austin, TX
qleak wrote:
eraldcoil wrote:
Show that is not there a function such that

Proof: (For )

It easy view:

1 for all .

By induction it is proved that for all ,

For It is trivial, If this is true for then:

As would be for ?

What? the way you've written it you want , why not just write that? And presumably you want and not the square of , otherwise it's trivial. In any case, clarify your function definition, it seems based on what you've written that you want just , which I sincerely doubt is the case, since you can just let be the (functional) square of the successor function if so.

functional square of the successor function is a fancy way of saying
f(n)=n+2 which has
f(f(n))=f(n+2)=(n+2)+2=n+4

Yes, but that isn't what he wants, at least not apparently, he wants to show that there is NO such function.

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 Post subject: Re: About a function over natural numbers which does not exiPosted: Mon, 28 Nov 2011 18:22:47 UTC
 Senior Member

Joined: Mon, 14 Feb 2011 22:39:36 UTC
Posts: 73
Location: Chile
eraldcoil wrote:
Show that is not there a function such that

Proof: (For )

It easy view:

1 for all .

By induction it is proved that for all ,

For It is trivial, If this is true for then:

As would be for ?

Top

 Post subject: Re: About a function over natural numbers which does not exiPosted: Mon, 28 Nov 2011 23:43:17 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12098
Location: Austin, TX
Why did you just quote your own post? Do you have something new to say?

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