Re: Wondering if my idea is right concerning Transfinite Sets

In article <19670998.1173395903081.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
Peter Whang <peter_junho@xxxxxxxxxxx> wrote:
Take the following series,
1,3,4,8,16,32,64,128,...
Where the first two numbers are 1 and 3 and the rest of them are 2^(n-1).

If we take a set containing exactly all the terms of the series, then cardinality of such set is equal to aleph-null. Since (aleph-null)+1 = (aleph-null) and each number is only finitely greater than 1, the sum of all those terms should equal aleph-null.

On the other hand, we can see that the sum of all first finite number of (n) terms is equal to 2^n (where n>1). If we expand its logic, we see: sum of all members of the series is 2^(aleph-null).

But then it exerts that aleph-null=2^aleph-null.

Is there a fault with the way i treated the transfinite numbers as sums of finite numbers? Please help me out on this one, because I still don't quite get the connection between finite and transfinite numbers

What this example shows is that if X is a set of ordinals, then:

sup {2^x | x in X}

might be different from:

2^(sup X)

--
Daniel Mayost

.

Relevant Pages

  • Re: Wondering if my idea is right concerning Transfinite Sets
    ... Peter Whang a écrit: ... But then it exerts that aleph-null=2^aleph-null. ... Please help me out on this one, because I still don't quite get the connection between finite and transfinite numbers ...
    (sci.math)
  • Wondering if my idea is right concerning Transfinite Sets
    ... But then it exerts that aleph-null=2^aleph-null. ... Is there a fault with the way i treated the transfinite numbers as sums of finite numbers? ... Please help me out on this one, because I still don't quite get the connection between finite and transfinite numbers ...
    (sci.math)