Liste des Groupes | Revenir à s logic |
Le 27/07/2024 à 14:55, Richard Damon a écrit :And who was using that set?On 7/27/24 8:16 AM, WM wrote:Mistake! ℕ U ω = {1, 2, 3, ..., ω}Le 27/07/2024 à 13:27, Richard Damon a écrit :On 7/27/24 7:13 AM, WM wrote:>Le 27/07/2024 à 04:23, Richard Damon a écrit :>
>By your logic, if you take a set and replace every element with a number that is twice that value, it would by the rule of construction say they must be the same size.>
That is true in potential infinity. But I assume actual infinity.>
So, what part is not true?
In potential infinity there is no ω.
>Are you stating that replacing every element with another unique distinct element something that make the set change size?>
In actual infinity the number of elements of any infinite set is fixed.
Doubling all elements of the set ℕ U ω = {2, 4, 6, ..., ω}
But what number became ω when doubled?See the correction.yields the set>
{2, 4, 6, ..., ω, ω+2, ω+4, ..., ω*2}.
>
Why?
But why? we were talking about the infinite set of the Naturals.>I know. Therefore I wrote ℕ U ω, or better ℕ U {ω}.
Note, ω is NOT a member of the Natural Numbers, it is just the "least upper bound" that isn't in the set.
Which isn't a Natural Number, as if it was, then that set of Natural Numbers would have a maximun member and be finite.>There is no definable natural number ω/2. But if there are all elements, then there is no gap before ω but ω-1.
There is no Natural Number that is ω/2 so that doubling it get you to ω, as every Natural Number when doubled gets you another Natural Number.
And thus you can't have ω-1, just like you can't have -1 in the Natural Numbers.>No, it is the first transfinite number like 0 is the first non-positive number.
Your "logic" just seems to be that ω is just some very big, an perhaps unexpressed, value of a Natural Number,
The fact that your theory is inconsistant makes it wrong.>The fact that you can't understand this is deplorable but does not make my theory wrong.
Using the unit fractions itelligent readers understand that there must be a first one after zero. Others must believe in the magical appearance of infinitely many unit fractions.Nope, since that implies there is a highest Natural Number, which breaks their definition,
Regards, WM
Les messages affichés proviennent d'usenet.