After serious thinking sergio wrote :
> On 3/2/2022 8:11 PM, Chris M. Thomasson wrote:
>> On 2/28/2022 3:26 PM, FromTheRafters wrote:
>>> Chris M. Thomasson has brought this to us :
>>>> On 2/28/2022 1:02 AM, FromTheRafters wrote:
>> [...]
>>>> Humm... Theoretically there can be a sequence of infinite dice rolls that
>>>> just happen to perfectly equal pi? Is that okay to even ponder on?
>>>
>>> The way I look at it, if you can describe the exact real number
>>> formulaically, then there is a guaranteed exact place on the real number
>>> line for it. A randomly generated string of digits for the fractional part
>>> does not describe any particular number, but a place is guaranteed for
>>> whatever it is.
>>
>> Agreed!
>
>
>
> Like the lockers at the train station! (well, sort of..)

The bus station at the Hilbert Hotel has as many lockers as it needs
but still is almost all of them empty after using only the countable
ones and a few transcendentals. :)

On 2/10/2022 8:22 AM, WM wrote:
> FromTheRafters schrieb am Donnerstag, 10. Februar 2022 um 12:28:46 UTC+1:
>> WM wrote :
>
>>> Cantor has not shown anything for the complete set. Each of his indexes has
>>> almost all indexes as successors.

wrong. the index formula applies to ALL, each and every, numbers

>> You still appear to assume that 'complete' means 'has a maximum'.
>
> Not at all. It means: Nothing is left.

this is not a store with biscuits.

>
>> Complete here, to me, just means each and every element of one set is
>> uniquely paired (one-to-one) with each and every element of the other
>> set, none unaccounted for -- not that there is a last such element in
>> any such set.
>
> Complete means that all elements are paired and nothing is left. When Cantor's sequence is complete,
>
> k = (m + n - 1)(m + n - 2)/2 + m
> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
>
> then we can write it into the first column,
>
> 1/1, __, __, __, ...
> 1/2, __, __, __, ...
> 2/1, __, __, __, ...
> 1/3, __, __, __, ...
> 2/2, __, __, __, ...
> ...
> and nothig remains in the other columns.

So you took the matrix of rational numbers, wrote the rationals indexed with natural numbers in the first column, and then zeroed out the rest of the
matrix ?

Why ?

>
>>> Infinite processes don't need to "end"... they just need a way to continue.
>>> [JMoravitz in
>>> https://math.stackexchange.com/questions/4377025/at-closer-inspection-the-concept-of-countability-shows-problems-how-to-solve]
>> I don't see how that relates to mappings.
>
> Either it relates to mappings or mappings can be complete.

its unrelated.

>>
>> To me, all numbers have infinite representations with associated
>> formulae (or process) which is where their values actually reside.
>
> Yes, the formulas are the heart of the number. There is no infinite representation of anything.

too general, be specific

>
>> We
>> simply choose to call endless sequences of zero or nine in CDE as being
>> 'terminated'. Our algorithms end simply because we finite beings need
>> them to, and we make it so, and we often accept 'close enough'
>> approximations to the actual value contained in the formula.
>
> That is analysis. Cantor needs precision. Nothing must be left alone.

Which he does with his indexing, precision, one to one mapping.

>>
>> Seems opposite to what the quote says,
>
> The quote is an insufficient attempt to defend Cantor's claims. It switches to potential infinity whereas Cantor explicitly claimed actual or finished or completed infinity.

see? the quote sucks. So does you matrix, which is not a matrix

>
> Regards, WM
>

On 2/10/2022 8:22 AM, WM wrote:
> FromTheRafters schrieb am Donnerstag, 10. Februar 2022 um 12:28:46 UTC+1:
>> WM wrote :
>
>> You still appear to assume that 'complete' means 'has a maximum'.
>
>> Complete here, to me, just means each and every element of one set is
>> uniquely paired (one-to-one) with each and every element of the other
>> set, none unaccounted for -- not that there is a last such element in
>> any such set.
>
> Complete means that all elements are paired and nothing is left. When Cantor's sequence is complete,
>
> k = (m + n - 1)(m + n - 2)/2 + m
> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
>
>> I don't see how that relates to mappings.
>
>>
>> To me, all numbers have infinite representations with associated
>> formulae (or process) which is where their values actually reside.
>
>> We
>> simply choose to call endless sequences of zero or nine in CDE as being
>> 'terminated'. Our algorithms end simply because we finite beings need
>> them to, and we make it so, and we often accept 'close enough'
>> approximations to the actual value contained in the formula.
>
>>
>> Seems opposite to what the quote says,
>
>
> Regards, WM
>
>