Re: Real Number Paradox?




On 22/06/2005 23:14, William Elliot wrote:

> On Wed, 22 Jun 2005, Jean-Claude Arbaut wrote:
>> On 22/06/2005 02:28, William Elliot wrote:
>>
>>>>> Also infinitesimals of non-standard analysis.
>>>>
>>>> But looking for them in R is not very wise ;-)
>>>>
>>> Hey look! Newton did it and not only did he get away with it,
>>> he was declared genius.
>>
>> He certainly did not. He died long before sets were invented by Cantor.
>> For all the new and fundamental ideas he had at this time, he was a genius.
>> But seeing physicist stuck with methods dating from 16th century is a pain
>> ;-)
>>
> To 1/N0 = { 0,1/n | n in N } add the infinitesimal a and to the subspace
> topology of 1/N0 add the open set { 0,a }. a is an element that's
> in between 0 and 1/N = (1/N0)\0

Here "a" is merely a symbol, and certainly not a real number.
So I reapeat: "looking for them in R is not very wise".


>>> For the time being
>>> integral quibble dt = waste(t)
>>> Therefore
>>> quibble = dwaste(t)/dt

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