New Paradox for the "Principles of Physics".

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I reject the assertion in your last sentence. Show us a good reason why it should be so. Infinity is not an integer, yet the number of integers is infinite. How is that not a counterexample to your asseretion? It exactly parallels the status of eternal existence with respect to forms. -|Tom|-

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You're making a puzzling analogy. I cannot see what infinity has to do with my statement. Are you trying to divert this discussion to a debate to Cantorian infinite sets?

1. If one defines as EXISTENCE the set of all things that exist, then EXISTENCE must be a member of that set, simply because it also exists. This is an obvious, common sense definition.

2. If all member of the set EXISTENCE must have a cause then EXISTENCE also must have a cause.

3. If all members of the set EXISTENCE have a cause except EXISTENCE then EXISTENCE is an antinomy. Simply it does not obey the rules of the set it defines.

Now, you got some choice here:

1. Abolish your causality principle
2. Accept that existence has a cause
3. Abolish your creation ex nihilo principle

One thing is for sure: you must do something, something other than diverting the discussion from REAL issues into IMAGINARY issues such as Cantorian infinite sets and mathematics of infinite. But even then, you are wrong. Infinite sets are not antinomies, just abstract concepts. In your case we're talking about a serious violation of the principles of logic by devicing self-contradictory statements and claiming they are slef-evident truths.




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Yes, this is very good. Basically formalized and summarized what I was trying to say in my very inefficient way.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[123...]: If the numberline is infinitely long, infinity itself should be a finite integer. For the number line to be infinite, there has to be an infinitely large number.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

Both of these sentences are wrong on their face, more or less by definition of "infinity". [Infinity -- concept of being always unlimited: the concept of being unlimited by always being larger than any imposed value or boundary.]

All integers are finite.
The number of integers is infinite.

With which of these staements do you disagree, and why?

As I said earlier, learning to use infinities in mathematics and in logic requires some discipline to avoid fallacies. I highly recommend Gamow's "One, Two, Three ... Infinity", which made this subject easy for me when I was still in high school. -|Tom|-

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>
<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[123...]: If the numberline is infinitely long, infinity itself should be a finite integer. For the number line to be infinite, there has to be an infinitely large number.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

Both of these sentences are wrong on their face, more or less by definition of "infinity". [Infinity -- concept of being always unlimited: the concept of being unlimited by always being larger than any imposed value or boundary.]

All integers are finite.
The number of integers is infinite.

With which of these staements do you disagree, and why?

As I said earlier, learning to use infinities in mathematics and in logic requires some discipline to avoid fallacies. I highly recommend Gamow's "One, Two, Three ... Infinity", which made this subject easy for me when I was still in high school. -|Tom|-



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I disagree with your statement that the number of integers is infinite if infinity isn't a finite number. When I add two integers, the sum is another integer. When I add 3 integers, the sum is another integer. Why should this relationship, that every sum of integers leads to another integer ever break down no matter how many integers I added? When you call the number line infinite, you are invoking a number to represent that quality. This number is the sum of all the numbers in the set. But if every sum leads to another number, it has to be a member of its own set.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[123...]: I disagree with your statement that the number of integers is infinite if infinity isn't a finite number.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

I repeat the definition: <font color=orange>Infinity -- concept of being always unlimited: the concept of being unlimited by always being larger than any imposed value or boundary.</font id=orange>

In what way does the number of integers fail to fulfill this definition? In what way is it limited?

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>Why should this relationship, that every sum of integers leads to another integer ever break down no matter how many integers I added?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

It doesn't ever break down. No one suggested that it did. When we say that the number of integers is infinity, that certainly does not make infinity an integer or the sum of any integers or groups of integers, however large. The whole point is that the number of integers goes beyond any integer you can name, write, or even imagine. The number of integers is "unlimited". The same cannot be said for sums of integers or counts of integers in any group.

The trick here is for you to familiarize with the use of infinity in math and physics. First, study 1/0. Examine its properties. Then learn the difference between "infinite" and "indeterminate". Then learn the math of infinities (where <img src=icon_infty.gif border=0 align=middle> == infinity; xdt == indeterminate): <img src=icon_infty.gif border=0 align=middle>+<img src=icon_infty.gif border=0 align=middle>=<img src=icon_infty.gif border=0 align=middle>; <img src=icon_infty.gif border=0 align=middle>-<img src=icon_infty.gif border=0 align=middle>=xdt; <img src=icon_infty.gif border=0 align=middle>*<img src=icon_infty.gif border=0 align=middle>=<img src=icon_infty.gif border=0 align=middle>; <img src=icon_infty.gif border=0 align=middle>/<img src=icon_infty.gif border=0 align=middle>=xdt; <img src=icon_infty.gif border=0 align=middle>^<img src=icon_infty.gif border=0 align=middle>=<img src=icon_infty.gif border=0 align=middle>2, a higher order of infinity; etc. Then learn how these concepts and infinities and infiniteesimals in general arise in derivitives and integrals in calculus, and how useful they are. Finally, study singularities and physical phenomena such as the "ultraviolet xatastrophe" to see how this applies to physics.

It's a tall order. But if you really want to understand how concepts such as dimensions and the universe can be infinite, this is all essential background. Wouldn't those of you you have this background agree?

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>When you call the number line infinite, you are invoking a number to represent that quality. This number is the sum of all the numbers in the set. But if every sum leads to another number, it has to be a member of its own set.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

I don't agree with any of these three statements. Infinity is not a member of the set of numbers. -|Tom|-

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[George]: The set of all numbers is not infinite and there are not an infinite amount of integers since there are really only 10 contained in the set, {0,1,2,3,4,5,6,7,8,9}. All numbers can be made from this set of 10 and any "new" number is simply a duplication of what already is, nothing new.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

The first ten integers are called "digits", George. The number of integers is infinite.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>Tom, why can't you simply admit defeat? You are wrong, you know you are wrong, you have been shown that you are wrong, and plus <u>this isn't even your own idea/concept</u>. Accept the fact that some peoples logic is better than yours. Obviously you are very knowledgeable and smart but your logic is inferior. Tear down your model and rebuild it, but first you need to admit error. Come on Tom, admit it! It will make you feel better.
Actually, I'll put it this way. If you don't admit you are wrong then I don't see how I can participate on this board any longer.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

Make a logical argument about the subject, or hold your peace. Comments about participants are not welcome on this Board. If you don't agree with that, perhaps it is time for you to take a break. -|Tom|-

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>As fer them commets bout participants I has no thoughts to what you are talkin bout. Are you simply looking for a reason to have this thread erased?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

Please see "Plaudits and Pundits" forum, "Courtesy and Decorum" topic, especially item #1. -|Tom|-