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Re: [obm-l] Bijeção
- To: obm-l@xxxxxxxxxxxxxx
- Subject: Re: [obm-l] Bijeção
- From: "Nicolau C. Saldanha" <nicolau@xxxxxxxxxxxxxx>
- Date: Fri, 9 Nov 2007 22:57:13 -0200
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On Nov 9, 2007 8:30 PM, Victor Magri <dcpiyou@xxxxxxxxxxx> wrote:
>
> Olá amigos,
>
> Gostaria de saber como se pode estabelecer uma bijeção entre o
> conjunto dos números naturais e racionais postivos
Seja N = {0,1,2,3,...}, N* = {1,2,3,...}.
Primeiro defina uma bijeção f:N->Z.
Por exemplo, f(n) = n/2 se n for par e -(n+1)/2 se n for ímpar.
Agora defina g: N* -> Q+ por g(2^e2*3^e3*...*p^ep*...) =
2^f(e2)*3^f(e3)*...*p^f(ep)*...
Assim g(60) = g(2^2*3^1*5^1) = 2^f(2)*3^f(1)*5^f(1) = 2^1*3^(-1)*5^(-1) = 2/15.
N.
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