Re: Replacement of Cardinality (infinite middle)

On 08/08/2024 03:30 AM, FromTheRafters wrote:

on 8/8/2024, WM supposed :

Le 08/08/2024 à 00:17, Moebius a écrit :
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Actually, his "thinking process" is simple:
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"Since there is a gap (space) between adjacent unit fractions and all
unit fractions are in the interval (0, 1], there must be FINITELY
MANY of them (i.e. a first/smallest one)."

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No, that is nonsense. There are not finitely many unit fractions.

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Then stop assuming that there is a first and last element.

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Of course, you can start with a first and last element,
then make infinitely-many in the middle.
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0 ... ( ... infinitely-many ... ) ... infinity