We might all be NPCs in the game of life.

georg jetson said:

Science has it's limitations, but it's still fun as hell to find out what they are... right?

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Absolutely. It is also fun to find out that things that were previously thought impossible are in fact, possible.

carolina guy said:

If the universe is infinite (by definition, it is), then it just means that the leading edge of what we are perceiving is getting closer to infinite, but (also by definition) we will also never perceive the boundaries of the universe, because (by definition) they do not exist.

Also, if the currently perceivable edge of reality is over 15 billion light years away, we have no method of realistically knowing if that boundary (created by an alleged "big bang") has changed its movements/momentum dramatically (+ or -) since. Simply put, we are dealing with mathematics and theories that do not work in an infinite system.

We cannot even test light speed outside our own gravity well to know if the current theories even hold water...much less even fully define gravity in or out of our gravity well.

Click to expand...

Something can be finite in size, but I infinite in scope. Think about that balloon again. Creatures on it can travel infinitely, but that surface is quite finite. Such is likely the case with our universe if the theory that it is a surface on a higher dimensional object is correct.

BTW, there are mathematically magnitudes of infinity. Not that such applies in the case at hand.

The best example of this would be some sets of numbers. Consider the set of Integers. It can be broken down into two sets of numbers: Even Integers and Odd Integers. Each set contains half the elements of the superset, yet all three sets are infinite in size!

Even larger is the set of Real Numbers, of which all three are subsets. Furthermore, the three subsets are countably infinite. The set of Real Numbers is uncountable, introducing another order of magnitude.


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<o>

eye95 said:

Something can be finite in size, but I infinite in scope. Think about that balloon again. Creatures on it can travel infinitely, but that surface is quite finite. Such is likely the case with our universe if the theory that it is a surface on a higher dimensional object is correct.

BTW, there are mathematically magnitudes of infinity. Not that such applies in the case at hand.

The best example of this would be some sets of numbers. Consider the set of Integers. It can be broken down into two sets of numbers: Even Integers and Odd Integers. Each set contains half the elements of the superset, yet all three sets are infinite in size!

Even larger is the set of Real Numbers, of which all three are subsets. Furthermore, the three subsets are countably infinite. The set of Real Numbers is uncountable, introducing another order of magnitude.


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Click to expand...

Well...consider these set sizes:

Positive Integers = infinite
Negative Integers = infinite
All Integers = infinite
Real Numbers = infinite

Or

Number of Positive Integers = Number of Negative Integers = Number of All Integers = Number of Real Numbers

Logically, this makes sense and doesn't make sense for the simple reason that our perceptions, and therefore our theories and mathematical systems cannot handle the concept of infinity.

I believe that whether the set is countable or uncountable is functionally irrelevant when the size reaches infinite because the end state cannot be determined. This is where the theories fail when meeting reality.

Actually, there is one flaw in your post. The number of Integers is not equal to the number of Real Numbers. All the sets of Integers you mention can be put into one-to-one correspondences with each other that would cover every number in both sets in any correspondence. Such could not be said for any set of Integers and the set of Reals.


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eye95 said:

Actually, there is one flaw in your post. The number of Integers is not equal to the number of Real Numbers. All the sets of Integers you mention can be put into one-to-one correspondences with each other that would cover every number in both sets in any correspondence. Such could not be said for any set of Integers and the set of Reals.


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<o>

Click to expand...

Ah...but you forget the basics...

If A=B, and B=C, then A=C

No, I did not. A may equal B, but neither equals C. All the sets of Integers that you mention are equal in size. None of them is equal in size to the set of Reals.


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eye95 said:

No, I did not. A may equal B, but neither equals C. All the sets of Integers that you mention are equal in size. None of them is equal in size to the set of Reals.


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<o>

Click to expand...

Are they infinite in size?

carolina guy said:

If the universe is infinite (by definition, it is), then it just means that the leading edge of what we are perceiving is getting closer to infinite, but (also by definition) we will also never perceive the boundaries of the universe, because (by definition) they do not exist.

Also, if the currently perceivable edge of reality is over 15 billion light years away, we have no method of realistically knowing if that boundary (created by an alleged "big bang") has changed its movements/momentum dramatically (+ or -) since. Simply put, we are dealing with mathematics and theories that do not work in an infinite system.

We cannot even test light speed outside our own gravity well to know if the current theories even hold water...much less even fully define gravity in or out of our gravity well.

Click to expand...

6^6^6 is different from (6^6)^6

Might be close enough to infinite.

eye95 said:

No, I did not. A may equal B, but neither equals C. All the sets of Integers that you mention are equal in size. None of them is equal in size to the set of Reals.


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<o>

Click to expand...

I understand that (by theory) that there are an infinite number of "real" numbers between the positive integer 1 and positive integer 2. Of course, there is no method to verify this, and then the mathematics fail when you consider infinity * 2 when you move to the positive integer 3 and consider the number of "real" numbers between 1 and 3, which clearly, must be twice as many as between 1 and 2. So, you either have:

Number "real" numbers between Positive Integer 1 and Positive Integer 2 = Infinitely Large Total #1 (call this A)
Number "real" numbers between Positive Integer 2 and Positive Integer 3 = Infinitely Large Total #2 (call this B)

Infinitely Large Total #1 + Infinitely Large Total #2 = Infinitely Large Sum #1 (call this C)
A + B = C


Does A = B ?
Does A + B = C ?

Does C = 2 * A or C = 2 * B ?

Infinity is Infinity, no matter how it is sliced or diced.


Or...


You have a paradox.

No paradox. The set of Reals can be put into a one-to-one relationship with the set of Reals between any two real numbers.

Those two sets are the same size as each other. All the sets of Integers we have mentioned are the same size as each other. None of the sets of Integers is the same size as any of the sets of Reals mentioned.

Let me throw another set of numbers into the mix that is even larger than the set of Reals: The set of Complex Numbers, which is actually a set of ordered Pairs of real number. This set cannot be put into a one-to-one correspondence with any of the previously mentioned sets.

Anyway, you and I are making the same point: Something infinite in size can become larger!


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To support eye95's point:
[video=youtube;elvOZm0d4H0]Infinity is bigger than you think[/video]

Tawnos said:

To support eye95's point:
[video=youtube;elvOZm0d4H0]Infinity is bigger than you think[/video]

Click to expand...

I know I said I'm done with this thread but infinity does not exist. It would take more information than exists in the universe to create.

For example, let's assume you can really always add 1 more to something, at some point the number (even if written in plancks) would be larger than all matter and energy.

Infinity is not real.

BTW, not to cloud the issue, but to hopefully add just a touch of clarity: The difference between countable sets and uncountable sets is EXACTLY the same difference as between the discrete and the continuous I mentioned above.

Ya know, the English language even recognizes this conceptual distinction. It is the difference between many and much, fewer and less, and the like.