Broken Circle

I'm sorry guys, I guess Frederick Cantor, Bernhard Reimann and all the rest of the mathematicians that established all this decades ago didn't have the benefit of your insight. Perhaps you could all write an article to Mathematics Quarterly and enlighten all the mathematicians as to how they have been fooled all these years. The next thing you'll be telling me is that transcendental and complex numbers are all nonsense too.

How many ways can it be said? There is no last number infinity, one can only point to a finite instance of a member of a set of integers. Infinity is the cardinality of the set and you cannot mix them together as you continually do. I started with a comment about the infinite extent of temporality but Mac wants infinity to be ALL THERE IS which is as vague as anything I am being accused of. I won't have my specific comment diverted into a plethora of subsidiary issues that have nothing to do with what I commented on. The issue stands, if temporality is finite then one must invoke miracles to explain how time suddenly came into existence and will miraculously disappear at some later date. I notice that no one ever answers this point directly or even acknowledges it.

123.. and Mac
I in no way regard inf+1 as being any more "self-contradictory" than n/0 being undefined. If you want to throw it out then doing so results in a mountain of contradictions elsewhere. 1 can be added to a complex number also, is that operation invalid because they are two totally different types of number? In inf+1 infinity is NOT an integer, it is a cardinality and you always have to keep that in mind.

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I'm sorry guys, I guess Frederick Cantor, Bernhard Reimann and all the rest of the mathematicians that established all this decades ago didn't have the benefit of your insight. Perhaps you could all write an article to Mathematics Quarterly and enlighten all the mathematicians as to how they have been fooled all these years. The next thing you'll be telling me is that transcendental and complex numbers are all nonsense too.

How many ways can it be said? There is no last number infinity, one can only point to a finite instance of a member of a set of integers. Infinity is the cardinality of the set and you cannot mix them together as you continually do. I started with a comment about the infinite extent of temporality but Mac wants infinity to be ALL THERE IS which is as vague as anything I am being accused of. I won't have my specific comment diverted into a plethora of subsidiary issues that have nothing to do with what I commented on. The issue stands, if temporality is finite then one must invoke miracles to explain how time suddenly came into existence and will miraculously disappear at some later date. I notice that no one ever answers this point directly or even acknowledges it.

123.. and Mac
I in no way regard inf+1 as being any more "self-contradictory" than n/0 being undefined. If you want to throw it out then doing so results in a mountain of contradictions elsewhere. 1 can be added to a complex number also, is that operation invalid because they are two totally different types of number? In inf+1 infinity is NOT an integer, it is a cardinality and you always have to keep that in mind.


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Note that when you add two different types of numbers, you have to convert one to the other first. For example, 1/2 + 0.5 is nonsensensical unless you converted 1/2 to 0.5 or 0.5 to 1/2. So, at least if we are going to talk about infinities, we need to separate them into different types of infinities (e.g. rational, irrational, natural, etc.) before we operate on them. Now, how do we convert one type of infinity to another? But this is really a task in futility imo since infinity by definition is without bound. How can you add to something that is without bound?

Your first paragraph is a classic fallacy- appeal to authority. It is not a logical argument. How can you not consider infinity + 1 = infinity self-contradictory? Please explain how you add to a number that has no limits? Please provide the logic for "larger infinities".

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I won't have my specific comment diverted into a plethora of subsidiary issues that have nothing to do with what I commented on. The issue stands, if temporality is finite then one must invoke miracles to explain how time suddenly came into existence and will miraculously disappear at some later date. I notice that no one ever answers this point directly or even acknowledges it.
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Call it a miracle if you want but it could actually be how Nature really works. What if the state of "nothing" is a condition for something to come into existence? Once there is something, the condition of "nothing" can no longer be achieved, so it becomes an irreversible process.

Just look at every physical processes around you- they are all irreversible. Once something has changed forms in the universe, the universe can't go back to the same form. " All the king's men couldn't put Humpty Dumpty back
together again" - remember that old saying? Well, that is a key
to understanding how something can come from nothing but the reverse isn't true.

An alternative model could go like this: everything that exists in our universe is actually popping into and out of existence at every instant in time. "Nothing" becomes the condition for "something", but reciprocally, "Something" becomes the condition for "nothing".
The problem I have with this idea is the that of continuity- how can something that goes out of existence remember who, what and where it was to retain continuity when it comes back into existence?

But in both cases, I would take a "miracle" over a circular argument any day.

Patrick,

"Eternal Energy" has a different meaning than "Infinite Energy". "Eternal Energy" would seem to say that the "energy" exists forever, it cannot be destroyed where "Infinite Energy" would seem to imply that there is an unlimited quantity.[unquote]


Ans: I agree with the distinction of definition between Infinity and Eternal. HOwever, Eternal invokes the concept of "Infinite Time" as well so to be eternal implies Infinite existance regardless of quantity.


Jeremy,

Your appeal to authority and historical accepted concepts does not answer "Where did your (1) more guest come from, if infinite quests (All there could be) have already registered?

123..., is absolutely right here:

Note that when you add two different types of numbers, you have to convert one to the other first. For example, 1/2 + 0.5 is nonsensensical unless you converted 1/2 to 0.5 or 0.5 to 1/2. So, at least if we are going to talk about infinities, we need to separate them into different types of infinities (e.g. rational, irrational, natural, etc.) before we operate on them. [unquote]

You are mixing units without first defining a common denominator.

Saying Infinity + 1 = Infinity does not mean that you can find a (1) to add. It tends to mean infact just the opposite.


123....,

You are precisely right here:

Call it a miracle if you want but it could actually be how Nature really works. What if the state of "nothing" is a condition for something to come into existence? Once there is something, the condition of "nothing" can no longer be achieved, so it becomes an irreversible process.[unquote]

But I disagree that we should call our lack of understanding a miracle.

Accidentally hit button twice - deleted copy of previous.

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Note that when you add two different types of numbers, you have to convert one to the other first. For example, 1/2 + 0.5 is nonsensensical unless you converted 1/2 to 0.5 or 0.5 to 1/2. So, at least if we are going to talk about infinities, we need to separate them into different types of infinities (e.g. rational, irrational, natural, etc.) before we operate on them. Now, how do we convert one type of infinity to another?
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Sorry to disappoint but your analogy from one type of number to another does not hold because the different types do not share all the same properties. Infinity + ANY number of lesser cardinality is by definition infinity, there is no need for conversions.

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But this is really a task in futility imo since infinity by definition is without bound. How can you add to something that is without bound?
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Because you are adding to a CARDINALITY not a specific finite number. If you could add to it in the sense you describe it would become something other than infinity which by your own protests it cannot be. What is the contradiction in that?

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Your first paragraph is a classic fallacy- appeal to authority. It is not a logical argument. How can you not consider infinity + 1 = infinity self-contradictory? Please explain how you add to a number that has no limits? Please provide the logic for "larger infinities".
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I am going to reiterate what Tom has already said elsewhere. This is a physical science board. If you guys want to read Raymond Smullyan and inundate people with logic puzzles and attack the cornerstones of mathematics than do it on a math oriented board where you can do battle with professional mathematicians. I have explained twice now how one adds to infinity and both explanations are probably not accepted. I am not going to explain the logic for larger infinities because it is not my ambition or task to act as math professor and tutor everyone. If you want the details then take a class or get a book. Since no one here seems to accept basic mathematics I see very little common ground for debate.