asimovian
June 12th, 2002, 12:44 PM
At least, that's what I think.
And that's why I would like a little input from you people on this little problem here.
If my English is not totally correct, please be patient.
Consider the set of natural numbers, i.e. 1, 2, 3... It tends towards infinity as we go on counting, that is to say, it doesn't stop at any particular number. These are the numbers which we use to count things in the physical universe (i.e. 1 cloud, 2 clouds, 3 clouds...1 dollar, 2 dollars, 3 dollars... :) ).
Now let's take a different kind of set, namely one in which each number is the inverse of each analogous natural number (i.e. 1/1, 1/2, 1/3...). This set, too, is an infinite set, that should be pretty obvious, as you can go on dividing 1 by succeeding natural numbers infinitely.
The first set goes together with the physical universe. What's typical for the physical universe, is that it consists of objects you can count.
This second set however is a little bit more tricky : if the first one is the one characterizing the physical universe, then what is the second one about ?
(Remark : please notice that, although both of these sets of numbers are infinite, it does not seem to be the same 'kind' of infinity : you will see what I mean if you try adding up, first the numbers of the first set (but don't forget to stop at some particular point !) and then (separately of course) add up a few of the numbers of the second set.
You will see that, although the total goes toward infinite, it does not increase in the same way)
And that's why I would like a little input from you people on this little problem here.
If my English is not totally correct, please be patient.
Consider the set of natural numbers, i.e. 1, 2, 3... It tends towards infinity as we go on counting, that is to say, it doesn't stop at any particular number. These are the numbers which we use to count things in the physical universe (i.e. 1 cloud, 2 clouds, 3 clouds...1 dollar, 2 dollars, 3 dollars... :) ).
Now let's take a different kind of set, namely one in which each number is the inverse of each analogous natural number (i.e. 1/1, 1/2, 1/3...). This set, too, is an infinite set, that should be pretty obvious, as you can go on dividing 1 by succeeding natural numbers infinitely.
The first set goes together with the physical universe. What's typical for the physical universe, is that it consists of objects you can count.
This second set however is a little bit more tricky : if the first one is the one characterizing the physical universe, then what is the second one about ?
(Remark : please notice that, although both of these sets of numbers are infinite, it does not seem to be the same 'kind' of infinity : you will see what I mean if you try adding up, first the numbers of the first set (but don't forget to stop at some particular point !) and then (separately of course) add up a few of the numbers of the second set.
You will see that, although the total goes toward infinite, it does not increase in the same way)

