Re: abundance of irrationals!)

Randy Poe said:
>
> 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.
I am trying to figure out what high school let you graduate without being able
to read or think. Probably some kind of parochial school.......

>
> The only thing I can come up with is that you really can't
> distinguish between element size and set size.
I can and do distinguish, and also note the relationship between them if there
is any. In the case of the naturals, there is, and you choose to ignore it.
Deliberate ignorance is foolishness.
>
> 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?
Duh.
>
> 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}?
Duh.
>
> 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?

You can't get the idea that there is a finite difference between each
successive pair of naturals can you? This means in the set each takes a finite
space on the number line. So, and infinite number of them takes an infinite
amount of space. What is space between two points on the number line? The
difference between the values of those two points. If the points are infinitely
far away from each other on this infinite line, then there is an infinite
difference between them. Since a finite minus a finite is always finite, one of
those point MUST have infinite value. If you can't get this simple proof, then
go into history or some other non-logical study. Take up belly dancing or
something like that on your intellectual level.
>
> - Randy
>
>

--
Smiles,

Tony
.

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