B Infinite vs Expanding Universe: A Physics Conundrum Explained

[jbriggs444]

Would you say that infinity of natural numbers is quite small among infinities?

You would have to define "small" in this context. And give a threshold for "quite". It is not clear how one would compare the infinite cardinality of the natural numbers with the positive infinity in the two-point compactification of the real numbers.

In any case, this is irrelevant to the discussion at hand.

 

[phinds]

Would you say that infinity of natural numbers is quite small among infinities?

Google "hierarchy of infinities"

 

[Comeback City]

Would you say that infinity of natural numbers is quite small among infinities?

It is quite similar to infinity of whole numbers

 

[phinds]

It is quite similar to infinity of whole numbers

I don't get "similar". Since both are cardinalities of sets then either they have the same Aleph number, in which case they are identical not similar, or they have diffrerent Aleph numbers, in which case they are different (and not similar).

 

[Comeback City]

I don't get "similar". Since both are cardinalities of sets then either they have the same Aleph number, in which case they are identical not similar, or they have diffrerent Aleph numbers, in which case they are different (and not similar).

Well, infinity + 1 = infinity, so I'm going to read some more about infinity!

 

[phinds]

Well, infinity + 1 = infinity

Yes, Aleph1 + 1 = Aleph1 and Aleph2 +1 = Aleph2. That does NOT make Aleph1 identical to, or similar to, Aleph2

, so I'm going to read some more about infinity!

Good idea. That will likely dispel your misunderstanding.

 

[Comeback City]

that has nothing at all to do with your statement

Good idea. That will likely dispel your misunderstanding.

You should read more about "comic relief"

 

[phinds]

You should read more about "comic relief"

Doesn't that have something to do with Billy Crystal and Whoopie Goldberg? They are not infinite.

 

[Comeback City]

Doesn't that have something to do with Billy Crystal and Whoopie Goldberg? They are not infinite.

Yeah you got me again

 

[Ken G]

This is not true. Not every physics theory has to have problems.

I never said a physics theory has to have problems, I said they are all known to be incomplete. Which is true.

 

[Ken G]

Hi Ken. What are your thoughts on when we can reasonably say that the predictions of GR probably aren't correct?

I don't think we can say when a prediction probably isn't correct, we simply have to test it. What is the track record of theories that we thought were probably not correct, versus ones we probably thought were? It's cherry picking, but still I'd say that track record is not good at all. For example:
We thought for thousands of years that geocentric models were probably correct and would not significantly change in the future.
We thought for hundreds of years that Galilean relativity was probably correct, so when Maxwell's equations treated the speed of light as a constant of the theory, most physicists thought that had to be incorrect.
Eddington thought that Chandrasekhar's theory of white dwarfs was probably incorrect because it predicted a maximum mass, above which no static solution was possible without drastic changes to the star. He reasoned that something missing from Chandrasekhar's approach would guarantee stability.
Einstein thought that quantum mechanics had to be wrong because it violated local realism.
And so on.

 

[Comeback City]

Yes, Aleph1 + 1 = Aleph1 and Aleph2 +1 = Aleph2. That does NOT make Aleph1 identical to, or similar to, Aleph2

So do the infinite sets of natural numbers and whole numbers have the same or different Aleph numbers? Wikipedia is saying that natural numbers have an Aleph number of 0 (Aleph-naught). It doesn't mention whole numbers, but whole numbers are just natural numbers with 0. Is it safe to assume infinite series of whole numbers also has Aleph number of 0?

 

[phinds]

So do the infinite sets of natural numbers and whole numbers have the same or different Aleph numbers? Wikipedia is saying that natural numbers have an Aleph number of 0 (Aleph-naught). It doesn't mention whole numbers, but whole numbers are just natural numbers with 0. Is it safe to assume infinite series of whole numbers also has Aleph number of 0?

Yes, they are the same. It's the reals, as I recall, that is the first instance of Aleph1

 

[jbriggs444]

Yes, they are the same. It's the reals, as I recall, that is the first instance of Aleph1

The continuum hypothesis is the statement that the cardinality of the reals is Aleph 1. Its truth or falsity is not decidable (under the usual axioms of set theory).

 

[nikkkom]

For quite a number of various kinds of infinities, look here:

https://en.wikipedia.org/wiki/Ordinal_number