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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Sat, 19 Oct 2024 15:21:19 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sat, 19 Oct 2024 15:38:53 +0200 schrieb WM:
> On 19.10.2024 14:20, Alan Mackenzie wrote:
>> WM <wolfgang.mueckenheim@tha.de> wrote:
>>> On 17.10.2024 23:22, Alan Mackenzie wrote:
>>>> WM <wolfgang.mueckenheim@tha.de> wrote:

>>> When doubling natural numbers we obtain even numbers which have not
>>> been doubled.
>>> This is a sentence that every mathematician can understand.
>> It is not - it is ill formed and ambiguous.  It doesn't say which
>> natural numbers are being doubled.
> That is not said because it is true for all sets of natural numbers.
> Your critique is therefore not justified but due to your lack of
> comprehension.
It is not true for infinite sets.

>>  It is unmathematical in that it
>> seems to posit a doubling being done one element at a time
> Wrong again. Even all natural numbers can be multiplied by 2.
You seem unable to imagine that.

>> rather than the standard mathematical concept of a mapping from N -> N
>> where n is mapped to 2n.  In this standard notion, all numbers are
>> doubled, and we encounter no undoubled even natural numbers.
> Therefore the standard notion is wrong, if the natural numbers are a
> set.
"if"

> The interval occupied by the numbers is doubled when all numbers are
> multiplied by 2. If even the second half, which has not been multiplied,
You just said all numbers are multiplied. What is the "second half"?

> contains natural numbers, then there are more after the
> procedure than before. Hence the "set" has changed and therefore is not
> a set. Note that sets do not change.
Tell that the potential infinity.

>>> It is true because the interval covered by the doubled numbers is
>>> twice as large as the interval covered by the numbers to be doubled.
>> The interval is infinite.  "Doubling" an infinite set yields a set of
>> the same size as the original - there is a 1-1 correspondence between
>> them.
> Multiplying n by 2 does not yield the same number.
> Multiplying all n by 2 does not yield the same numbers.
In part it does. All even numbers are also naturals.
  {1, 2, 3, 4} n 2*{1, 2, 3, 4}
= {1, 2, 3, 4} n   {2, 4, 6, 8}
= {2, 4}


-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.