>> In article <PM0004CCA66AD92...@ac814669.ipt.aol.com>,
>> See.ab...@aol.com (jmfbahciv) writes:

>>> Charles Richmond wrote:

>>>> The Fundamental Theorem of Arithmetic states that every integer
>>>> greater than 1 is either a prime itself or a product of primes,
>>>> and that each such integer has a unique prime factorization.
>>>> It is sometimes called the Unique Factorization Theorem.

>>> Ah!  Ok.  I have never played with that one.  It might be
>>> interesting to create a system where that Theorem is not true.

>> I'm sure some politician (a finance minister, most likely)
>> would be able to provide you with an example.

> Not a prime minister?

>>> Charles Richmond wrote:

>>>> The Fundamental Theorem of Arithmetic states that every integer
>>>> greater than 1 is either a prime itself or a product of primes,
>>>> and that each such integer has a unique prime factorization.
>>>> It is sometimes called the Unique Factorization Theorem.

>>> Ah!  Ok.  I have never played with that one.  It might be
>>> interesting to create a system where that Theorem is not true.

>> I'm sure some politician (a finance minister, most likely)
>> would be able to provide you with an example.

> Not a prime minister?

> >>> [snip]

> >>>>Good.  I think the most elegant programming in apps is based on tables.
> >>>>I get almost as good a chill down my spine thinking about that kind
> >>>>of code as when I think about the Fundamental Theorem of Calculus.

> >>>      I like the Fundamental Theorem of Arithmetic myself.

> >> That's a new one to me.

> > The Fundamental Theorem of Arithmetic states that every integer greater than
> > 1 is either a prime itself or a product of primes, and that each such
> > integer has a unique prime factorization.  It is sometimes called the Unique
> > Factorization Theorem.

> Ah!  Ok.  I have never played with that one.  It might be interesting to
> create a system where that Theorem is not true.

> /BAH

>> On 2012-10-22, Charlie Gibbs <cgi...@kltpzyxm.invalid> wrote:

>>> In article <PM0004CCA66AD92...@ac814669.ipt.aol.com>,
>>> See.ab...@aol.com (jmfbahciv) writes:

>>>> Charles Richmond wrote:

>>>>> The Fundamental Theorem of Arithmetic states that every integer
>>>>> greater than 1 is either a prime itself or a product of primes,
>>>>> and that each such integer has a unique prime factorization.
>>>>> It is sometimes called the Unique Factorization Theorem.

>>>> Ah!  Ok.  I have never played with that one.  It might be
>>>> interesting to create a system where that Theorem is not true.

>>> I'm sure some politician (a finance minister, most likely)
>>> would be able to provide you with an example.

>> Not a prime minister?

> No, they're usually too busy with the Big Picture, i.e. setting
> themselves up as dictator.

> [snip]

>><GRIN>  So I would have to take a trip across the pond to hand you
>>$110.  Sounds a tad expensive.  I'll remember though for the time when
>>I move to eternal-september.org.

>      eternal-september.org is free.
>                                ^
>      Note the R.

>> [snip]

>>><GRIN>  So I would have to take a trip across the pond to hand you
>>>$110.  Sounds a tad expensive.  I'll remember though for the time when
>>>I move to eternal-september.org.

>>      eternal-september.org is free.
>>                                ^
>>      Note the R.

> I will pay for what I use.  I don't want them to disappear because
> everyone stopped sending money to them.

>>Ah!  Ok.  I have never played with that one.  It might be interesting to
>>create a system where that Theorem is not true.

>it would then not be arithmetic anymore. I think that given
>the group and ring assumptions under addition and multiplication
>you always end up with the unique factorization...but my memory
>is rusty and ought b verified.

>>Ah!  Ok.  I have never played with that one.  It might be interesting to
>>create a system where that Theorem is not true.

> it would then not be arithmetic anymore. I think that given
> the group and ring assumptions under addition and multiplication
> you always end up with the unique factorization...but my memory
> is rusty and ought b verified.

> >>Ah!  Ok.  I have never played with that one.  It might be interesting to
> >>create a system where that Theorem is not true.

> > it would then not be arithmetic anymore. I think that given
> > the group and ring assumptions under addition and multiplication
> > you always end up with the unique factorization...but my memory
> > is rusty and ought b verified.

> ONe thing I haven't done is group and ring math.

> Or set theory.  I still have to find the category theory book
> and go through that.

> /BAH

>    You have a large fenced area of tall grass inside which is a lion,
>your problem is to find the lion.

>    Build a fence bisecting the area, let a victi^Wvilla^Wvolunteer
>into each half.

> [snip]

>> Hmm, now that reminds me of the teacher who introduced us to
>>binary search under the name lion hunting roughly as follows.

>> You have a large fenced area of tall grass inside which is a lion,
>>your problem is to find the lion.

>> Build a fence bisecting the area, let a victi^Wvilla^Wvolunteer
>>into each half.

>     What do you do about a lion who sticks around the spawning
> point^W^Wplace where you build the fence?

> [snip]

> >       Hmm, now that reminds me of the teacher who introduced us to
> >binary search under the name lion hunting roughly as follows.

> >       You have a large fenced area of tall grass inside which is a
> >       lion,
> >your problem is to find the lion.

> >       Build a fence bisecting the area, let a victi^Wvilla^Wvolunteer
> >into each half.

>      What do you do about a lion who sticks around the spawning
> point^W^Wplace where you build the fence?

>> And the categorical ways of catching a lion, including catching him in
>> a moment of inertia.

>    Hmm, now that reminds me of the teacher who introduced us to
> binary search under the name lion hunting roughly as follows.

>    You have a large fenced area of tall grass inside which is a lion,
> your problem is to find the lion.

>    Build a fence bisecting the area, let a victi^Wvilla^Wvolunteer
> into each half.

>    Wait for a scream - repeat starting with the half you now know
> contains the lion. Continue until the fenced area is small enough to just
> contain one lion.

>    He was a maths teacher, so the next step was some numbers and a
> question about how many victi^Wvilla^Wvolunteers get killed before the lion
> is trapped.

>    It'll be on one side or another after the fence is built, fence
> builders are either immune to lion attack or in infinite supply and
> disposable.

> >       It'll be on one side or another after the fence is built, fence
> > builders are either immune to lion attack or in infinite supply and
> > disposable.

> When the lion attacks, you've found it. Or it's found you, without using
> a binary search.

>> On 11/14/2012 01:48 AM, Ahem A Rivet's Shot wrote:
>>> On Tue, 13 Nov 2012 17:15:36 -0800
>>> Gene Wirchenko <ge...@ocis.net> wrote:
>>>>        What do you do about a lion who sticks around the spawning
>>>> point^W^Wplace where you build the fence?

>>>    It'll be on one side or another after the fence is built, fence
>>> builders are either immune to lion attack or in infinite supply and
>>> disposable.

>> When the lion attacks, you've found it. Or it's found you, without using
>> a binary search.

>    No it has found the vict^Wvilla^Wvolunteer who is now dead and
> unable to report on the position of the lion.

> >> On 11/14/2012 01:48 AM, Ahem A Rivet's Shot wrote:
> >>> On Tue, 13 Nov 2012 17:15:36 -0800
> >>> Gene Wirchenko <ge...@ocis.net> wrote:
> >>>>        What do you do about a lion who sticks around the spawning
> >>>> point^W^Wplace where you build the fence?

> >>>       It'll be on one side or another after the fence is built,
> >>> fence builders are either immune to lion attack or in infinite supply
> >>> and disposable.

> >> When the lion attacks, you've found it. Or it's found you, without
> >> using a binary search.

> >       No it has found the vict^Wvilla^Wvolunteer who is now dead and
> > unable to report on the position of the lion.

> A good binary search reports an early success when it finds the lion.
> The log2(N) is when there is no lion.

>>> When the lion attacks, you've found it. Or it's found you, without using
>>> a binary search.

>>     No it has found the vict^Wvilla^Wvolunteer who is now dead and
>> unable to report on the position of the lion.

> A good binary search reports an early success when it finds the lion.
> The log2(N) is when there is no lion.