Re: Infinity =/= Infinity

albstorz@xxxxxx wrote:
> stephen@xxxxxxxxxx wrote:
>> albstorz@xxxxxx wrote:
>> > Proginoskes wrote:
>> >> albstorz@xxxxxx wrote:
>> >> > Infinity =/= Infinity
>> >> >
>>
>> >>
>> >> All true.
>> >>
>> >> > Ergo:
>> >> > This contradiction
>> >>
>> >> What contradiction? There is no stated contradiction.
>>
>>
>> > The contradiction: You have to put infinite many stones on the heap to
>> > have all finite numbers,
>>
>> True.
>>
>> > but there are not infinite many stones on it
>> > because if there are infinite many on the heap, this means an infinite
>> > number which doesn't exist.
>>
>> Why do you think that? You seem to be confusing the set
>> with elements of the set. Let's replace 'infinite' with
>> 'unending', and be real careful about when we are talking
>> about sets and when we are talking about elements.
>>
>> 'if there is an unending collection of stones, this means
>> an unending number which doesn't exist.'
>>
>> Why does the fact that the collection of stones never ends
>> mean that one of the numbers must also not end (whatever
>> it would mean for a number not to end)? No individual
>> stone (or number) is equivalent to the entire collection,
>> so insisting that because the entire collection has a property
>> that one of the stones must also have that property seems unfounded.


> Not one stone, all stones. Only if one of the stones has the number
> "#Infinity" labeld on it, there are infinitly many in.

No. None of the stones have #Infinity labelled on them.
There is no last stone. That is what infinity means.
Why do you think an unending collection of items should
have an end?

You seem to be the one who cannot distinguish between
potential and actual infinity. Mathematics handles
such distinctions just fine.

> Because we think
> the set exists as totality.

What do you mean by 'exists as totality'? Sets do
not physically exist. It sounds like you are claiming
that once we say 'all the rocks' we require a last rock
to spring into existence. Why?

Stephen
.

Relevant Pages

  • Re: Infinity =/= Infinity
    ... > number 1, two stones together for the number 2, and so on. ... we take stones from a stock and put them on a heap. ... > It is easy to say, as we need infinite stones. ...
    (sci.math)
  • Re: Infinity =/= Infinity
    ... There is no stated contradiction. ... You have to put infinite many stones on the heap ...
    (sci.math)
  • Re: Infinity =/= Infinity
    ... There is no stated contradiction. ... You have to put infinite many stones on the heap to ...
    (sci.math)
  • Re: Infinity =/= Infinity
    ... >>> that one of the stones must also have that property seems unfounded. ... That is what infinity means. ... >> the set exists as totality. ... > that once we say 'all the rocks' we require a last rock ...
    (sci.math)
  • Infinity =/= Infinity
    ... We consider the natural numbers as sets of stones. ... we take stones from a stock and put them on a heap. ... as we need infinite stones. ...
    (sci.math)
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