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  I'd assume that if we limit the length of a "word" to 26 letters,  the
answer
  would be 26 to the 26th power. This doesn't mean all the combinations
would
  be pronounceable by any given population. As an English speaker, I have
  trouble with African words that begin with "ng." But at least in theory,
one
  could imagine a population able to pronounce any of the words. Whether to
  make some accommodation for how many consonants can fall in a sequence, or
  how many vowels a "word" has to have might be moot. Languages (e.g.,
Biblical
  Hebrew) have been written without vowels).

But there the vowels were still implied, no? Anyway, for added thrill, you
can add tonality (different meanings depending on pitch) and forget about 26
letters. Language like Finnish, German and Dutch produce very long words
indeed, because whenever we combine two words we just add them together.
German is even better at that than Dutch, but the difference isn't too big.
One of the more famous Dutch words for that is
"Hottentottententententoonstellingstenten". It's a bit silly, but it's a
word anyway - (something like "tents for a Hottentot tent exhibition").
Anyway, the number of possible words gets rather big anyway. More
interesting to determine the possible number of theoretical sentences you
can produce. But that's not your point ...

My point is, that if this is your idea of an infinite set, I don't think it
actually is, unless you want to set no limit on the number of letters in a
word.

I think he actually means to give examples of large but limited sets, rather
than infinte, which are all examples of problems which can be solved by
brute force.

  pat

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Narrow" lang=3D0=20
  size=3D3 FAMILY=3D"SANSSERIF"><BR><STRONG>I'd assume that if we limit =
the length=20
  of a "word" to 26 letters, &nbsp;the answer <BR>would be 26 to the =
26th power.=20
  This doesn't mean all the combinations would <BR>be pronounceable by =
any given=20
  population. As an English speaker, I have <BR>trouble with African =
words that=20
  begin with "ng." But at least in theory, one <BR>could imagine a =
population=20
  able to pronounce any of the words. Whether to <BR>make some =
accommodation for=20
  how many consonants can fall in a sequence, or <BR>how many vowels a =
"word"=20
  has to have might be moot. Languages (e.g., Biblical <BR>Hebrew) have =
been=20
  written without vowels).&nbsp;</STRONG><SPAN =
class=3D527315721-12032001><FONT=20
  color=3D#0000ff face=3DArial =
size=3D2>&nbsp;</FONT></SPAN></FONT></FONT></DIV>
  <DIV><FONT face=3Darial,helvetica><FONT color=3D#000000 face=3D"Arial =
Narrow" lang=3D0=20
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<DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN =
class=3D527315721-12032001>But=20
there the vowels were still implied, no? Anyway, for added thrill, you =
can add=20
tonality (different meanings depending on pitch) and forget about 26 =
letters.=20
Language like Finnish, German and Dutch produce very long words indeed, =
because=20
whenever we combine two words we just add them together. German is even =
better=20
at that than Dutch, but the difference isn't too big. One of the more =
famous=20
Dutch words for that is "Hottentottententententoonstellingstenten". It's =
a bit=20
silly, but it's a word anyway - (something like "tents for a Hottentot =
tent=20
exhibition"). Anyway, the number of possible words gets rather big =
anyway. More=20
interesting to determine the possible number of theoretical sentences =
you can=20
produce. But that's not your point ...</SPAN></FONT></DIV>
<DIV><FONT face=3Darial,helvetica><FONT color=3D#000000 face=3D"Arial =
Narrow" lang=3D0=20
size=3D3 FAMILY=3D"SANSSERIF"><BR><STRONG>My point is, that if this is =
your idea of=20
an infinite set, I don't think it <BR>actually is, unless you want to =
set no=20
limit on the number of letters in a <BR>word.&nbsp;<BR></STRONG><SPAN=20
class=3D527315721-12032001><FONT color=3D#0000ff face=3DArial=20
size=3D2>&nbsp;</FONT></SPAN></FONT></FONT></DIV>
<DIV><FONT color=3D#0000ff face=3DArial lang=3D0 size=3D2 =
FAMILY=3D"SANSSERIF"><SPAN=20
class=3D527315721-12032001>I think he actually means to give examples of =
large but=20
limited sets, rather than infinte, which are all examples of problems =
which can=20
be solved by brute force.&nbsp; </SPAN></FONT></DIV>
<BLOCKQUOTE=20
style=3D"BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; PADDING-LEFT: =
5px">
  <DIV><FONT face=3Darial,helvetica><FONT color=3D#000000 face=3D"Arial =
Narrow" lang=3D0=20
  size=3D3 FAMILY=3D"SANSSERIF"><SPAN=20
  =
class=3D527315721-12032001>&nbsp;</SPAN><BR><STRONG>pat</STRONG></FONT>=20
  </FONT></DIV></BLOCKQUOTE></BODY></HTML>

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