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Topic: Infinity: The Story So Far
Replies: 298   Last Post: Apr 7, 2014 7:30 AM

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fom

Posts: 1,968
Registered: 12/4/12
Re: Infinity: The Story So Far
Posted: Feb 26, 2014 5:21 PM
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On 2/26/2014 3:17 PM, mueckenh@rz.fh-augsburg.de wrote:
> On Wednesday, 26 February 2014 20:44:49 UTC+1, fom wrote:
>> The set of natural numbers however is not every countable set but a very special countable set. The Peano axioms fail to produce this set because they are too general. They produce the set 1, S1, SS1, ...
>>

>>> Some of the many sets produced are
>>
>>> 1, 1s, 1ss, ...
>>
>>> 1, 11, 111, ...
>>
>>> 1, 1^1, 1^1^1, ...
>>
>>> and if someone happens to have defined, or simply to know, the natural numbers, then they produce also
>>
>>> 1, 1/2, 1/3, ...
>>
>>> 1, 1^2, 1^3, ...
>>
>>> and with good luck
>>
>>> 1, 2, 3, ...
>
>>
>>
>> A little bit of humor today?

>
> Humor? 1/3 - 1/2 is not 1. The set of natural numbers is not the same as all sets isomorphic to Peano's set. You cannot define the natural numbers without addition of 1. That's all.
>


I had been referring to the remark that
you might manage to get the *actual*
natural numbers from among the rest
with a little bit of good luck.

:-)






Date Subject Author
2/25/14
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Read Re: Infinity: The Story So Far
Dan Christensen
3/6/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/6/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
Wizard-Of-Oz
3/11/14
Read Re: Infinity: The Story So Far
Martin Shobe
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
Martin Shobe
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
Martin Shobe
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
Martin Shobe
3/12/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/12/14
Read Re: Infinity: The Story So Far
Martin Shobe
3/12/14
Read Re: Infinity: The Story So Far
ross.finlayson@gmail.com

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