Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

On 10/11/2024 3:15 PM, Richard Damon wrote:

On 10/11/24 3:29 PM, Chris M. Thomasson wrote:

On 10/11/2024 4:06 AM, Richard Damon wrote:

On 10/10/24 11:19 PM, Chris M. Thomasson wrote:

On 10/10/2024 6:38 PM, Richard Damon wrote:

On 10/10/24 2:32 PM, WM wrote:

On 09.10.2024 21:13, Alan Mackenzie wrote:

WM <invalid@no.org> wrote:

Am 09.10.2024 um 18:12 schrieb Alan Mackenzie:

WM <wolfgang.mueckenheim@tha.de> wrote:

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You've misunderstood the nature of N.  The set is not
{1, 2, 3, ..., ω}, it is {1, 2, 3, ...}.

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I use ℕ U {ω} for clarity.

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You would do better not to do so.  It gives wrong results.

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It gives unfamiliar results because you have no clear picture of actual infinity. If all natnumbers are there and if 2n is greater than n, then the doubled numbers do not fit into ℕ. But note, that is only true if all natnumbers do exist.

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No, *YOU* don't understand what actual infinity is like as you picture it just like the finite, but bigger.
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If not all do exist, te doubling yields larger natnumbers, some of which have not existed before. But that means potential infinity.

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But there aren't any natural numbers that have not existed before. That is just showing that your "actual infinity" is a finite set that you grabbed on the way to infinity, but didn't get there yet.
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Actual infinity means you need to wait until you get there. The problem is finite creatures can't do that, so can't handle actual infinity.

[...]
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What do you mean? I can say all the natural numbers. That was pretty fast for all of them. ;^)
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Which names the set, but not actually list the contents of that set.

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Who's counting anyway? lol. Infinite is infinite and finite is, well, finite... ;^) Just because we are finite beings does not negate the infinite, right?

 Right, but it means we lack some of the ability to actually PERCEIVE the reality of the infinite.

That's interesting to me because it kind of reminds me of 2d vs 3d vs 4d observers. Us 3d beings can look down at a 2d beings world and see all of it. A 4d being can look at our 3d world and see all of it. Think of a 4d being at a location in n-ary space that has a non-zero 4d component to its vectors. We would not be able to see it because is off axis in a higher dimension. However, it can see us, right through us, all the way down... Anyway, just thinking out loud here. Sorry! ;^o

 When one tries to do that, it is too easy to presume characteristics of the infinite are just like the finite, when they aren't (like having "ends").
 When we start by studing the processes that generate the infinite, we can build an understand of it, which while we can not directly perceive the infinite, we can understand it.
 When WM decides to ignore the logic, but just try squinting real hard to directly make out the infinite, he sees things that aren't, and thhus comes to wrong conclusions.