Re: INFINITY Revisited

Don Whitehurst <whit0911@xxxxxxx> wrote:
> Peter Webb wrote:
> <snip>
> DW wrote
>> > Does the list of natuarl numbers corresponding to the infinite set of
>> > natural numbers enumerate all of the digits dj where j = 1 -> oo of
>> > 1/3 = 0.333... ?
>> >
> Peter Webb wrote:
>>
>> No. 1/3 doesn't appear in the listas you have written it. It appears in
>> others, such as the standard mapping of p/q to Natural numbers.
>>
>>
>> >
>> > <snip>
>> >
>> > Can the set of natural numbers be put in a one to one correspondence
>> > with all of the digits of any specific decimalic number (including any
>> > nonterminating rational or irrational number)?
>> >
>>
>> Yes, trivially.
>>
>> 1 -> 3
>> 2 -> 1
>> 3 -> 4
>> 4 -> 1
>> 5 -> 5
>>
>> If you want a mapping between N and approximations to pi, pick
>> 1 -> 3
>> 2 -> 3.1
>> 3 -> 3.14
>>
>> If you want pi on the list,
>>
>> 1 -> pi
>> 2 -> 3
>> 3 -> 3.1
>> 4 -> 3.14
>>
> Here is where I get lost. Above in essence you said that the infinite
> set naturals can "trivially" be placed in a one to one correspondence
> with all of the digits of pi; and yet you now seem to be suggesting
> there are not enough natural numbers in the infinite set of natural
> numbers for a mapping between N the approximations of pi and pi, unless
> pi is placed as an indivdual element corresponding
> to some finite natural (in other words pi cannot be the last element).
> Why not if the set of naturals is infinite?

pi cannot be the last element because there is no last element.
The set of naturals are infinite and so there is no last
natural number to map to pi.

Stephen
.

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