Re: 'Infinite aggregates' puzzle



John Jones wrote:
herbzet wrote:
John Jones wrote:

Is the infinity of a sequence greater than an infinity of an
aggregate? Here is a sequenced infinity:
1,2,3,4... infinity

And here is an aggregate or random infinity whose numerals just happen
to coincide with those of the numbered sequence (above),
1,2,3,4 ...infinity

Which infinity is greater?

I have a random collection of objects on my desk.

If I regard them in terms of weight, then a sequence of those objects
is implied.

If I regard them in terms of monetary value, a (possibly different)
sequence is implied.

I suggest that "a sequence", in the sense that you are using it,
is something that is imposed on an aggregate by our minds -- it
is a mental classification. An aggregate does not intrinsically
possess a sequence.

--
hz

Yes, an aggregate does not intrinsically possess a sequence.

Ok.

Yet it can exist of entities, just like a sequence.

Don't know what this sentence means, in particular the reference
of the pronomial "it".

So my question is, is an aggregate infinity greater than a sequenced
infinity of, say, the totality of natural numbers?

The standard answer is, it depends on the aggregates in question:
The aggregate of points on the surface of a sphere is greater than
the aggregate of natural numbers, whether we regard the naturals as
sequenced or unsequenced.

I don't think the imposition or recognition of some sequence
changes the cardinality of a given aggregate. As I have mentioned,
an aggregate may have different ways of being sequenced.

--
hz
.

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