Re: infinity

Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:

> David Kastrup said:
>> stevendaryl3016@xxxxxxxxx (Daryl McCullough) writes:
>>
>> > But aleph_0 is not a natural number, so it is incorrect to replace
>> > n by aleph_0. However, it is true that the size of the set
>> >
>> > { 1, 2, ... aleph_0 }
>> >
>> > is aleph_0.
>>
>> I think that this is an abuse of notation since it implies a sequence
>> ending in aleph_0. But aleph_0 is a singular disconnected value in
>> that set. It has no predecessor.
>>
>> So I'd rather write it as
>>
>> { aleph_0, 0, 1, 2, ... }
>>
>> Yes, this set has size aleph_0.
>>
> Well, you only say that because you believe {0,1,2,3...} has size aleph_0

Uh, there is nothing to "believe" here. That is the _definition_ of
aleph_0.

> and that aleph_0+1=aleph_0.

That's already interpreting it. I am assuming nothing of that, but it
is easy to see that the mapping
alpha_0 -> 0
0 -> 1
1 -> 2

is a proper bijection, as you can in this manner map
{aleph_0, 0, 1, 2 ...} to {0, 1, 2 ...} and back again.

> However, the way Daryl wrote it makes some sense.

Not really. alpha_0 has no predecessor in the set.

> Unfortunately, it seems he meant it the way you prefer, which
> doesn't solve anything.

What should it solve?

> When you have an infinite set with infinite members, the vast
> majority of the members are infinite.

Uh, nonsense. If you have a set with infinite members, whether the
set itself is infinite or not, the set has at least one infinite
member. That's all you can you say about it.

> You can't throw ina token infinite number and expect that to solve
> anything.

What did you want to have solved?

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
.

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