Re: abundance of irrationals!)


Tony Orlow (aeo6) wrote:
> Well, it makes me want to puke when people claim to have an infinite
number of
> finite marbles in a finite bag of marbles. If I claimed to have such
a bag,
> would you believe me, or would you look for a screw loose somewhere?

I'm trying to figure out what you might have heard to make
you think somebody talked about an infinite set as being
of finite size.

The only thing I can come up with is that you really can't
distinguish between element size and set size.

Let's start simply. Do you know that the set

{1}

and the set

{120293481093128914981720921847120398712098172394871209871234}

are both sets of exactly the same size, namely sets with
a single element?

Did you know that I can have a set of size 1 that contains
an infinitely large element, for instance a single one
of your infinite integers? Did you know that this set has
exactly the same "size" (cardinality) as the set {1}?

If you accept all that, where in the world did you hear
a statement that you think is equivalent to "infinitely
many marbles in a finite sized bag"? Do you think somebody
said N is a finite set, somebody besides you?

- Randy

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