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From: J�rgen Exner on 5 Mar 2010 20:15
sreservoir <sreservoir(a)gmail.com> wrote:
>On 3/5/2010 5:54 PM, Peter J. Holzer wrote:
>> There is no way to represent all numbers in a finite amount of memory of
>> course.
>
>there is no way to represent all numbers full stop.

This is becoming philosophical now, but you can represent any number. In
the worst case you simply use a verbal description. Granted, that
doesn't do you much good if you want to use that number in a calculation
on the computer, but it is possible to represent it because otherwise
you wouldn't be able to think of this number in the first place.

jue
From: Dr.Ruud on 5 Mar 2010 20:40
J�rgen Exner wrote:
> sreservoir <sreservoir(a)gmail.com> wrote:
>> On 3/5/2010 5:54 PM, Peter J. Holzer wrote:

>>> There is no way to represent all numbers in a finite amount of memory of
>>> course.
>>
>> there is no way to represent all numbers full stop.
>
> This is becoming philosophical now, but you can represent any number. In
> the worst case you simply use a verbal description. Granted, that
> doesn't do you much good if you want to use that number in a calculation
> on the computer, but it is possible to represent it because otherwise
> you wouldn't be able to think of this number in the first place.

I think you mean that number almost half way between 2 and 3.
;-)

--
Ruud
From: J�rgen Exner on 5 Mar 2010 20:44
"Dr.Ruud" <rvtol+usenet(a)xs4all.nl> wrote:
>J�rgen Exner wrote:
>> sreservoir <sreservoir(a)gmail.com> wrote:
>>> On 3/5/2010 5:54 PM, Peter J. Holzer wrote:
>
>>>> There is no way to represent all numbers in a finite amount of memory of
>>>> course.
>>>
>>> there is no way to represent all numbers full stop.
>>
>> This is becoming philosophical now, but you can represent any number. In
>> the worst case you simply use a verbal description. Granted, that
>> doesn't do you much good if you want to use that number in a calculation
>> on the computer, but it is possible to represent it because otherwise
>> you wouldn't be able to think of this number in the first place.
>
>I think you mean that number almost half way between 2 and 3.
>;-)

No, the other one, the one that is exactly a quarter of an epsilon
smaller.

jue
From: sreservoir on 5 Mar 2010 21:18
On 3/5/2010 8:44 PM, J�rgen Exner wrote:
> "Dr.Ruud"<rvtol+usenet(a)xs4all.nl> wrote:
>> J�rgen Exner wrote:
>>> sreservoir<sreservoir(a)gmail.com> wrote:
>>>> On 3/5/2010 5:54 PM, Peter J. Holzer wrote:
>>
>>>>> There is no way to represent all numbers in a finite amount of memory of
>>>>> course.
>>>>
>>>> there is no way to represent all numbers full stop.
>>>
>>> This is becoming philosophical now, but you can represent any number. In
>>> the worst case you simply use a verbal description. Granted, that
>>> doesn't do you much good if you want to use that number in a calculation
>>> on the computer, but it is possible to represent it because otherwise
>>> you wouldn't be able to think of this number in the first place.
>>
>> I think you mean that number almost half way between 2 and 3.
>> ;-)
>
> No, the other one, the one that is exactly a quarter of an epsilon
> smaller.

nah, it's actually a two ninths of an epsilon.

--

"Six by nine. Forty two."
"That's it. That's all there is."
"I always thought something was fundamentally wrong with the universe"
From: Keith Thompson on 5 Mar 2010 21:39
Jürgen Exner <jurgenex(a)hotmail.com> writes:
> sreservoir <sreservoir(a)gmail.com> wrote:
>>On 3/5/2010 5:54 PM, Peter J. Holzer wrote:
>>> There is no way to represent all numbers in a finite amount of memory of
>>> course.
>>
>>there is no way to represent all numbers full stop.
>
> This is becoming philosophical now, but you can represent any number. In
> the worst case you simply use a verbal description. Granted, that
> doesn't do you much good if you want to use that number in a calculation
> on the computer, but it is possible to represent it because otherwise
> you wouldn't be able to think of this number in the first place.

As long as we're being philosophical, being able to think of a number
is not a prerequisite for that number's existence.

The set of finite verbal descriptions is only countably infinite.
There are uncountably infinitely many real numbers.

There are also some lovely paradoxes, such as
"the smallest number that cannot be described in 61 characters".

--
Keith Thompson (The_Other_Keith) kst-u(a)mib.org <http://www.ghoti.net/~kst>
Nokia
"We must do something. This is something. Therefore, we must do this."
-- Antony Jay and Jonathan Lynn, "Yes Minister"
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