Thread View: can.rsc.mathsci
4 messages
4 total messages
Started by Willse
Mon, 11 Oct 1999 00:00
Letters in the Name function
Author: Willse
Date: Mon, 11 Oct 1999 00:00
Date: Mon, 11 Oct 1999 00:00
18 lines
899 bytes
899 bytes
All-
Consider the function (whose domain is members of the set Z*, the set of
nonnegative integers) defined by
LiN(x)={letters in the formal English name of x}
For example, LiN(8)=5, 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=LiN(x) if n=1, a_n=LiN(a_(n-1)) if n>1]=4
Travis J. Willse
sal-crumb@geocities.com
Re: Letters in the Name function
Author: Jim Dars
Date: Mon, 11 Oct 1999 00:00
Date: Mon, 11 Oct 1999 00:00
94 lines
3678 bytes
3678 bytes
This is a multi-part message in MIME format.
------=_NextPart_000_0045_01BF1443.47661520
Content-Type: text/plain;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
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$GA.234@cpmsnbbsa05>...
>All-
>
>Consider the function (whose domain is members of the set Z*, the set =
of
>nonnegative integers) defined by
>
>LiN(x)=3D{letters in the formal English name of x}
>
>For example, LiN(8)=3D5, because "eight" has five letters.
>
>LiN(x) for the first few values of {0,1,2,...} are
>{4,3,3,5,4,4,3,5,5,4,3...}.
>
>Prove (or disprove) that, regardless of the initial value of x,
>
>{lim n->+oo}[a_n=3DLiN(x) if n=3D1, a_n=3DLiN(a_(n-1)) if n>1]=3D4
>
>Travis J. Willse
>sal-crumb@geocities.com
>
>
>
------=_NextPart_000_0045_01BF1443.47661520
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
<!DOCTYPE HTML PUBLIC "-//W3C//DTD W3 HTML//EN">
<HTML>
<HEAD>
<META content=3Dtext/html;charset=3Diso-8859-1 =
http-equiv=3DContent-Type>
<META content=3D'"MSHTML 4.71.1712.3"' name=3DGENERATOR>
</HEAD>
<BODY>
<DIV><STRONG><FONT color=3D#0000ff size=3D4>Hi =
Travis,</FONT></STRONG></DIV>
<DIV><STRONG><FONT color=3D#0000ff size=3D4></FONT></STRONG> </DIV>
<DIV><STRONG><FONT color=3D#0000ff size=3D4>With little set theory =
knowledge I look=20
at</FONT></STRONG></DIV>
<DIV><STRONG><FONT color=3D#0000ff size=3D4></FONT></STRONG> </DIV>
<DIV>{lim n->+oo}[a_n=3DLiN(x) if n=3D1, a_n=3DLiN(a_(n-1)) if=20
n>1]=3D4<BR> </DIV>
<DIV> </DIV>
<DIV><STRONG><FONT color=3D#0000ff size=3D4>and wonder if =
"a_n" conveys a=20
meaning I'm not aware of --- would you define it? --- Even if this is a =
stupid=20
request.</FONT></STRONG></DIV>
<DIV><STRONG><FONT color=3D#0000ff size=3D4></FONT></STRONG> </DIV>
<DIV><STRONG><FONT color=3D#0000ff size=3D4>Best wishes, =
Jim</FONT></STRONG></DIV>
<DIV>Willse<GBTT@EMAIL.MSN.COM> wrote in message=20
<#mAdbiEF$GA.234@cpmsnbbsa05>...</DIV>>All-<BR>><BR>>Consi=
der the=20
function (whose domain is members of the set Z*, the set =
of<BR>>nonnegative=20
integers) defined by<BR>><BR>>LiN(x)=3D{letters in the formal =
English name=20
of x}<BR>><BR>>For example, LiN(8)=3D5, because "eight" =
has five=20
letters.<BR>><BR>>LiN(x) for the first few values of {0,1,2,...}=20
are<BR>>{4,3,3,5,4,4,3,5,5,4,3...}.<BR>><BR>>Prove (or =
disprove) that,=20
regardless of the initial value of x,<BR>><BR>>{lim =
n->+oo}[a_n=3DLiN(x)=20
if n=3D1, a_n=3DLiN(a_(n-1)) if n>1]=3D4<BR>><BR>>Travis J. =
Willse<BR>><A=20
href=3D"mailto:sal-crumb@geocities.com">sal-crumb@geocities.com</A><BR>&g=
t;<BR>><BR>></BODY></HTML>
------=_NextPart_000_0045_01BF1443.47661520--
Re: Letters in the Name function
Author: deal4428
Date: Thu, 21 Oct 1999 00:00
Date: Thu, 21 Oct 1999 00:00
58 lines
1988 bytes
1988 bytes
so x a member of *Z, x=five hundred fifty three billion nine hundred
seventy seven million seven hundred seventy seven thousand seven hundred
fifty seven
now LiN(x)
now what is a_n
and what is going to limit?
----- Original Message -----
From: Willse <gbtt@email.msn.com>
Newsgroups: can.rsc.mathsci
Sent: Monday, October 11, 1999 7:27 PM
Subject: Letters in the Name function
> All-
>
> Consider the function (whose domain is members of the set Z*, the set of
> nonnegative integers) defined by
>
> LiN(x)={letters in the formal English name of x}
>
> For example, LiN(8)=5, 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=LiN(x) if n=1, a_n=LiN(a_(n-1)) if n>1]=4
>
> Travis J. Willse
> sal-crumb@geocities.com
>
>
>
Willse <gbtt@email.msn.com> wrote in message
news:#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)={letters in the formal English name of x}
>
> For example, LiN(8)=5, 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=LiN(x) if n=1, a_n=LiN(a_(n-1)) if n>1]=4
>
> Travis J. Willse
> sal-crumb@geocities.com
>
>
>
Re: Letters in the Name function
Author: Willse
Date: Sat, 30 Oct 1999 00:00
Date: Sat, 30 Oct 1999 00:00
76 lines
2541 bytes
2541 bytes
deal4428-
> so x a member of *Z, x=five hundred fifty three billion nine hundred
> seventy seven million seven hundred seventy seven thousand seven hundred
> fifty seven
> now LiN(x)
a_1=LiN(553 977 777 757)=114
a_2=LiN(LiN(553 977 777 757))=LiN(114)=18
a_3=LiN(LiN(LiN(553 977 777 757)))=LiN(LiN(114))=LiN(18)=8
a_4=LiN(LiN(LiN(LiN(553 977 777
757))))=LiN(LiN(LiN(114)))=LiN(LiN(18))=LiN(8)=5
a_5=LiN(LiN(LiN(LiN(LiN(553 977 777
757)))))=LiN(LiN(LiN(LiN(114))))=LiN(LiN(LiN(18)))=Lin(LiN(8))=LiN(5)=4
a_n=LiN(4)=4 (n>5)
Travis J. Willse
sal-crumb@geocities.com
> now what is a_n
> and what is going to limit?
>
> ----- Original Message -----
> From: Willse <gbtt@email.msn.com>
> Newsgroups: can.rsc.mathsci
> Sent: Monday, October 11, 1999 7:27 PM
> Subject: Letters in the Name function
>
>
> > All-
> >
> > Consider the function (whose domain is members of the set Z*, the set of
> > nonnegative integers) defined by
> >
> > LiN(x)={letters in the formal English name of x}
> >
> > For example, LiN(8)=5, 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=LiN(x) if n=1, a_n=LiN(a_(n-1)) if n>1]=4
> >
> > Travis J. Willse
> > sal-crumb@geocities.com
> >
> >
> >
> Willse <gbtt@email.msn.com> wrote in message
> news:#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)={letters in the formal English name of x}
> >
> > For example, LiN(8)=5, 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=LiN(x) if n=1, a_n=LiN(a_(n-1)) if n>1]=4
> >
> > Travis J. Willse
> > sal-crumb@geocities.com
> >
> >
> >
>
>
Thread Navigation
This is a paginated view of messages in the thread with full content displayed inline.
Messages are displayed in chronological order, with the original post highlighted in green.
Use pagination controls to navigate through all messages in large threads.
Back to All Threads