(January 30, 2018 at 3:14 pm)KevinM1 Wrote: One of the (many) things I don't understand about Christianity is the notion of wanting Jesus to be your lord. To want to genuflect before him and be ruled over by him. As an American, the idea of a central, non-democratically elected leader is completely anathema to my beliefs, and it confuses me that so many self-proclaimed patriots here seem so willing to be lorded over in a divine sense. IMO, a beneficial dictator is still a dictator.

So, Christians of AF, why do you want to be lorded over by Jesus? Why is this something you desire?

People, generally, seem to want to be ruled over by someone better (subjectively); it as though they prefer the comfort of being informed of how to live and behave rather than bothering to be responsible for their own conscience or actions. It's an unnecessary comfort that exists even in the form of the 'Murican government, because people want to be conscientiously lazy.

(February 14, 2018 at 12:42 pm)SteveII Wrote:

(February 14, 2018 at 12:13 pm)Grandizer Wrote: You're NOT paying attention!

polymath is arguing similar to Sean Carroll, in that he's not sure if space/time is infinite or not, but the bet is that it is.

No, not the "bet". That implies a theory. There is no theory that gets past the illogical concept of an actual infinity. What you are describing is a hope (the word Sean Carroll used). And that hope is driven by one thing only: a desire to have no beginning that then requires an explanation other than naturalism. 

Quote:And I make no claim that what I hold to is scientific in its entirety. My personal view is logical but not necessarily completely supported by scientific evidence, though it also doesn't contradict it either. So it's absurd that you want us to post a scientific theory that says this is what is the case, when no one said anything about a scientific theory.

You have not shown that your personal view is logical. You don't have to post a scientific theory. You chose to post a video that brought that up. Post anything that shows that people believe an actual infinite number of real things is possible--from any reputable source.

http://www.iep.utm.edu/infinite/

---

(February 14, 2018 at 12:46 pm)SteveII Wrote:

(February 14, 2018 at 12:39 pm)polymath257 Wrote: I can add a few more.

infinity * infinity=infinity

infinity/5=infinity

infinity^infinity=infinity

5*infinity=infinity

Generally, division of infinity isn't defined. So, infinity/infinity isn't well defined. But if you divide an infinite set into a finite number of equal sized sets, each piece will be infinite.

I'm done with you because you seem incapable of having a discussion. You cannot hold up your end of anything. It has been a hundred posts of assertions and never addressing anything mentioned--just writing vague sentences that only you think applies to anything. 

I think there is still hope for Grandizer.

Where is the contradiction? Be specific. I have addressed the *logical* point. You have failed to address the issue of the *logical* possibility of a completed infinity.

Instead, you present some *paradoxes* that show how the infinite is different than the finite. But that is to be expected. Paradoxes are not contradictions.

@Lut
There's a certain ambiguity in making ones own decisions.  The consequences of getting it wrong can be frightening before the fact and exhausting after the fact.  Some people fundamentally doubt their own agency...and while I find it difficult to believe that anyone could be so incompetent...maybe they know themselves better, maybe they are.

I still can't rate it any higher than a child's fear of responsibility, regardless. That's just my opinion.

So it would seem that an important part of if a complete set of infinite numbers is to define what it means to be a complete set? We didn’t do very well with defining a point, can we please define this. How is it complete, but not indicating a stop or an end?

It appears to me, that these sets are just loosely defined, or openly defined but how does that translate to the real world, and how can that be completed if it is open?

(February 14, 2018 at 1:10 pm)RoadRunner79 Wrote: So it would seem that an important part of if a complete set of infinite numbers is to define what it means to be a complete set? We didn’t do very well with defining a point, can we please define this.  How is it complete, but not indicating a stop or an end?

It appears to me, that these sets are just loosely defined, or openly defined but how does that translate to the real world, and how can that be completed if it is open?

Well, to be complete means that we can tell exactly when something is in the list or not. For example, the number 1273749
is in the list 1,2,3,.... but the number 1.34 is not.

It is complete in the real world if everything in the list actually exists and we can tell exactly when something is in the list and when it is not.

(February 14, 2018 at 12:28 pm)polymath257 Wrote:

(February 14, 2018 at 11:25 am)SteveII Wrote: Hilbert's Hotel:

Imagine a hotel with a finite number of rooms. All the rooms are full and a new guest walks in and wants a room. The desk clerk says no rooms are available.

Now imagine a hotel that has an infinite number of rooms. All the rooms are filled up so an infinite number of guests. A new guest walks up and wants a room. All the clerk has to to do is to move the guest in room #1 to room #2 and the guest from #2 to #3 and so on so your new guest can have a room #1. You can do this infinite number of times to a hotel that was already full.

Now imagine instead the clerk moves the guest from #1 to #2 and from #2 to #4 and from #3 to #6 (each being moved to a room number twice the original). All the odd number rooms become vacant. You can add an infinite number of new guests to a hotel that was full and end up with it half empty. 

How many people would be in the hotel if the guest in #1 checked out?

If everyone in odd number rooms checks out, how many checked out? How many are left?

Now what if all the guest above room number 3 check out. How many checked out? How many are left?

So from the above we get:
infinity + infinity = infinity
infinity + infinity = infinity/2
infinity - 1 = infinity
infinity / 2 = infinity
infinity - infinity = 3

Conclusion: the idea of an actual infinite is logically absurd.

The only one of these that is wrong is that last. Subtraction of infinities is not well defined. So yes, we have infinity+3=infinity, but that doesn't mean that infinity-infinity is well defined. In fact, since infinity+5=infinity also, that shows subtraction is NOT well defined.

None of the rest are actual contradictions, are they? They are merely differences between how finite things work and how infinite things work.

Even the fact that subtraction isn't well defined is just one of those differences between finite and infinite collections.

So? Where is the logical absurdity?

Besides the last example, all of the other examples seem akin to describing sequences (properties of sequences and subsequences) from the set of positive integers to the set (or subset) of positive integers along with describing that any countably infinite set will have the same cardinality as any other countably infinite set. 

Regarding indeterminate forms, any Calculus II text should cover them: infinity - infinity would be an example of an indeterminate form .  For example, if we take the limit of a function as that function approaches infinity and a direct substitution of infinity into that function yields infinity - infinity, then it is not guaranteed that a limit exists nor does the indeterminate form indicate what the limit is if it does exist, and so, it is not surprising that one would obtain a paradoxical result when trying to apply a concept that is not well defined in theory to reality.

There is a distinction between the indeterminate forms from calculus limits and the fact that subtraction of cardinals is not well defined. But infinity-infinity isn't well defined either way. Nor is infinity/infinity.

(February 14, 2018 at 12:57 pm)polymath257 Wrote:

(February 14, 2018 at 12:42 pm)SteveII Wrote: No, not the "bet". That implies a theory. There is no theory that gets past the illogical concept of an actual infinity. What you are describing is a hope (the word Sean Carroll used). And that hope is driven by one thing only: a desire to have no beginning that then requires an explanation other than naturalism. 


You have not shown that your personal view is logical. You don't have to post a scientific theory. You chose to post a video that brought that up. Post anything that shows that people believe an actual infinite number of real things is possible--from any reputable source.

http://www.iep.utm.edu/infinite/

Ah, a link!

I read it (and I think I have read it even before today). Nowhere in that entire article does it say anything about mathematicians or scientists believing that an actual infinite of concrete objects (or events) is possible. An infinite set is defined by its members and becomes its own thing. It is a useful fiction. There is nothing that relates it to the real word. Paste the section where you think I misunderstood. 

BTW, somewhere in there it actually said spacetime is finite according to big bang-type models.

(February 14, 2018 at 2:07 pm)SteveII Wrote:

(February 14, 2018 at 12:57 pm)polymath257 Wrote: http://www.iep.utm.edu/infinite/

Ah, a link!

I read it (and I think I have read it even before today). Nowhere in that entire article does it say anything about mathematicians or scientists believing that an actual infinite of concrete objects (or events) is possible. An infinite set is defined by its members and becomes its own thing. It is a useful fiction. There is nothing that relates it to the real word. Paste the section where you think I misunderstood. 

BTW, somewhere in there it actually said spacetime is finite according to big bang-type models.

Actually, it *does* say most believe it is not only possible, but in fact the case.

And yes, it is possible that space is finite. We do not know. Both finite and infinite are possibilities.

(February 14, 2018 at 2:34 pm)polymath257 Wrote:

(February 14, 2018 at 2:07 pm)SteveII Wrote: Ah, a link!

I read it (and I think I have read it even before today). Nowhere in that entire article does it say anything about mathematicians or scientists believing that an actual infinite of concrete objects (or events) is possible. An infinite set is defined by its members and becomes its own thing. It is a useful fiction. There is nothing that relates it to the real word. Paste the section where you think I misunderstood. 

BTW, somewhere in there it actually said spacetime is finite according to big bang-type models.

Actually, it *does* say most believe it is not only possible, but in fact the case.

And yes, it is possible that space is finite. We do not know. Both finite and infinite are possibilities.

Then it shouldn't be hard to cut and paste that section--for both of your points...I'll wait.