Re: Orlow cardinality question

Tony Orlow (aeo6) wrote:
> I believe you have missed much of this discussion. My Theory of Bigulosity
> exactly calculates what out intuitions ACTUALLY tell us: that adding an element
> increases the size of the set by one, that the even integers are exactly HALF
> of the integers, etc. This is not beyond reach, and should be regarded as
> progress, not rebellion. The goal is consistnecy, which is sorely lacking in
> cardinality.

You have not answered Jan's primary complaint about what you said.
Let's give it in finite terms first. Does multiplying every element by
2 give a smaller or larger set? Let's see:

{1,2,3}
{2,4,6}

So far so good

{1,2,3,4,5,6}
{2,4,6,8,10,12}

Hmm. It seems that I don't get a set that's half the size, why would
then I intuitively get half the set when I multiply {1,2,3,4,...} by 2?
I certainly have not added nor taken away any elements, I've just
relabeled them. Do I get a different set when I multiply every element
by 2 and yet a different one when I pick out just the even integers?
If so, I would like to know what do you mean by an "even number" since
it obviously can't be "a number with a divisor of 2". If this
intuition is not supposed to carry over to infinite sets, then why does
your bigulosity intuition carry over and not this one?

Jiri

.

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