Re: Letters in the Name function

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Article #28

#28

From: Jim Dars
Date: Mon, 11 Oct 1999 00:00

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Hi Travis,

With little set theory knowledge I look at

{lim n->+oo}[a_n=3DLiN(x) if n=3D1, a_n=3DLiN(a_(n-1)) if n>1]=3D4


and wonder if "a_n" conveys a meaning I'm not aware of --- would you =
define it? --- Even if this is a stupid request.

Best wishes, Jim
Willse wrote in message <#mAdbiEF$GA.234@cpmsnbbsa05>...
>All-
>
>Consider the function (whose domain is members of the set Z*, the set =
of
>nonnegative integers) defined by
>
>LiN(x)=3D{letters in the formal English name of x}
>
>For example, LiN(8)=3D5, because "eight" has five letters.
>
>LiN(x) for the first few values of {0,1,2,...} are
>{4,3,3,5,4,4,3,5,5,4,3...}.
>
>Prove (or disprove) that, regardless of the initial value of x,
>
>{lim n->+oo}[a_n=3DLiN(x) if n=3D1, a_n=3DLiN(a_(n-1)) if n>1]=3D4
>
>Travis J. Willse
>sal-crumb@geocities.com
>
>
>

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<META content=3Dtext/html;charset=3Diso-8859-1 =
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<BODY>
<DIV><STRONG><FONT color=3D#0000ff size=3D4>Hi =
Travis,</FONT></STRONG></DIV>
<DIV><STRONG><FONT color=3D#0000ff size=3D4></FONT></STRONG>&nbsp;</DIV>
<DIV><STRONG><FONT color=3D#0000ff size=3D4>With little set theory =
knowledge I look=20
at</FONT></STRONG></DIV>
<DIV><STRONG><FONT color=3D#0000ff size=3D4></FONT></STRONG>&nbsp;</DIV>
<DIV>{lim n-&gt;+oo}[a_n=3DLiN(x) if n=3D1, a_n=3DLiN(a_(n-1)) if=20
n&gt;1]=3D4<BR>&nbsp;</DIV>
<DIV>&nbsp;</DIV>
<DIV><STRONG><FONT color=3D#0000ff size=3D4>and wonder if =
&quot;a_n&quot; conveys a=20
meaning I'm not aware of --- would you define it? --- Even if this is a =
stupid=20
request.</FONT></STRONG></DIV>
<DIV><STRONG><FONT color=3D#0000ff size=3D4></FONT></STRONG>&nbsp;</DIV>
<DIV><STRONG><FONT color=3D#0000ff size=3D4>Best wishes, =
Jim</FONT></STRONG></DIV>
<DIV>Willse<GBTT@EMAIL.MSN.COM> wrote in message=20
&lt;#mAdbiEF$GA.234@cpmsnbbsa05&gt;...</DIV>&gt;All-<BR>&gt;<BR>&gt;Consi=
der the=20
function (whose domain is members of the set Z*, the set =
of<BR>&gt;nonnegative=20
integers) defined by<BR>&gt;<BR>&gt;LiN(x)=3D{letters in the formal =
English name=20
of x}<BR>&gt;<BR>&gt;For example, LiN(8)=3D5, because &quot;eight&quot; =
has five=20
letters.<BR>&gt;<BR>&gt;LiN(x) for the first few values of {0,1,2,...}=20
are<BR>&gt;{4,3,3,5,4,4,3,5,5,4,3...}.<BR>&gt;<BR>&gt;Prove (or =
disprove) that,=20
regardless of the initial value of x,<BR>&gt;<BR>&gt;{lim =
n-&gt;+oo}[a_n=3DLiN(x)=20
if n=3D1, a_n=3DLiN(a_(n-1)) if n&gt;1]=3D4<BR>&gt;<BR>&gt;Travis J. =
Willse<BR>&gt;<A=20
href=3D"mailto:sal-crumb@geocities.com">sal-crumb@geocities.com</A><BR>&g=
t;<BR>&gt;<BR>&gt;</BODY></HTML>

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From: "Jim Dars" <jim_dars@email.msn.com>
Subject: Re: Letters in the Name function
Date: 1999/10/11
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