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[SPAM] Res: [obm-l] racionais

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--0-409301131-1196171713=:45743
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vc quis dizer alfa =3D(2n+1)/2, acredito... de qualquer forma, existem muit=
os outros racionais que podem estar entre n e n+1 (ex: 25/18. 26/18, 35/18,=
 457/256.... todos est=C3=A3o entre 1 e 2; de fato, h=C3=A1 infinitos)=0A=
=0Ao problema =C3=A9: dado um racional p/q, provar que existe apenas um int=
eiro n tal que n<=3Dp/q<n+1=0A=0Aa =3D alfa=0A=0Asuponha q existe um k tal =
que k<=3Da<k+1 e k =3D/=3D n=0A=0Aseja n > k=0A=0Ase k<=3Da e n<=3Da =3D=3D=
> n-k<=3D0 =3D=3D> n<=3Dk, o que =C3=A9 uma contradi=C3=A7=C3=A3o (mesmo ar=
gumento para n<k)=0A=0Alogo n =3D k, o que prova a unicidade de n=0A=0A=0A-=
---- Mensagem original ----=0ADe: Kleber Bastos <kleber09@xxxxxxxxx>=0APara=
: obm-l@xxxxxxxxxxxxxx=0AEnviadas: Segunda-feira, 26 de Novembro de 2007 23=
:10:01=0AAssunto: [obm-l] racionais=0A=0A=0ASeja alfa um n=C3=BAmero racion=
al. Prove que existe um =C3=BAnico n=C3=BAmero inteiro n tal que n<=3Dalfa<=
n+1.=0A =0Apensei em alfa sendo o ponto m=C3=A9dio alfa=3D 2n+1/2 , ou seja=
 racional , e dai vejo que n =C3=A9 m=C3=ADnimo , mas como provo que n =C3=
=A9 =C3=BAnico ? =0A=0A-- =0AKleber B. Bastos=0A=0A=0A      Abra sua conta =
no Yahoo! Mail, o =C3=BAnico sem limite de espa=C3=A7o para armazenamento!=
=0Ahttp://br.mail.yahoo.com/
--0-409301131-1196171713=:45743
Content-Type: text/html; charset=utf-8
Content-Transfer-Encoding: quoted-printable

<html><head><style type=3D"text/css"><!-- DIV {margin:0px;} --></style></he=
ad><body><div style=3D"font-family:times new roman, new york, times, serif;=
font-size:12pt"><DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman=
, new york, times, serif">vc quis dizer alfa =3D(2n+1)/2, acredito... de qu=
alquer forma, existem muitos outros racionais que podem estar entre n e n+1=
 (ex: 25/18. 26/18, 35/18, 457/256.... todos est=C3=A3o entre 1 e 2; de fat=
o, h=C3=A1 infinitos)</DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: t=
imes new roman, new york, times, serif">&nbsp;</DIV>=0A<DIV style=3D"FONT-S=
IZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif">o problema=
 =C3=A9: dado um racional p/q, provar que existe apenas um inteiro n tal qu=
e n&lt;=3Dp/q&lt;n+1</DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: ti=
mes new roman, new york, times, serif">&nbsp;</DIV>=0A<DIV style=3D"FONT-SI=
ZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif">a =3D alfa<=
/DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new yo=
rk, times, serif">&nbsp;</DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY=
: times new roman, new york, times, serif">suponha q existe um k tal que k&=
lt;=3Da&lt;k+1&nbsp;e k&nbsp;=3D/=3D n</DIV>=0A<DIV style=3D"FONT-SIZE: 12p=
t; FONT-FAMILY: times new roman, new york, times, serif">&nbsp;</DIV>=0A<DI=
V style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, =
serif">seja n &gt; k</DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: ti=
mes new roman, new york, times, serif">&nbsp;</DIV>=0A<DIV style=3D"FONT-SI=
ZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif">se k&lt;=3D=
a e n&lt;=3Da =3D=3D&gt; n-k&lt;=3D0 =3D=3D&gt; n&lt;=3Dk, o que =C3=A9 uma=
 contradi=C3=A7=C3=A3o (mesmo argumento para n&lt;k)</DIV>=0A<DIV style=3D"=
FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif">&nbs=
p;</DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new=
 york, times, serif">logo n =3D k, o que prova a unicidade de n<BR><BR></DI=
V>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york,=
 times, serif">----- Mensagem original ----<BR>De: Kleber Bastos &lt;kleber=
09@xxxxxxxxx&gt;<BR>Para: obm-l@xxxxxxxxxxxxxx<BR>Enviadas: Segunda-feira, =
26 de Novembro de 2007 23:10:01<BR>Assunto: [obm-l] racionais<BR><BR>=0A<DI=
V>Seja alfa um n=C3=BAmero racional. Prove que existe um =C3=BAnico n=C3=BA=
mero inteiro n tal que n&lt;=3Dalfa&lt;n+1.</DIV>=0A<DIV>&nbsp;</DIV>=0A<DI=
V>pensei em alfa sendo o ponto m=C3=A9dio alfa=3D 2n+1/2 , ou seja racional=
 , e dai vejo que n =C3=A9 m=C3=ADnimo , mas como provo que n =C3=A9 =C3=BA=
nico ? <BR clear=3Dall><BR>-- <BR>Kleber B. Bastos </DIV></DIV>=0A<DIV styl=
e=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif"=
><BR></DIV></div><br>=0A=0A=0A      <hr size=3D1>Abra sua conta no <a href=
=3D"http://br.rd.yahoo.com/mail/taglines/mail/*http://br.mail.yahoo.com/";>Y=
ahoo! Mail</a>, o =C3=BAnico sem limite de espa=C3=A7o para armazenamento! =
=0A</body></html>
--0-409301131-1196171713=:45743--
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