Deeper than primes

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jsfisher said:
So your original assertion was dishonest. You made it when you had no evidence to support it.

Now that you have moved the goal posts, where is your proof of your new assertion? In particular, you'd need to refute the possibility that the mental illness was responsible for the obsession with mathematics.
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Again serial only-thinking style, isn't it jsfisher?.

Real Complexity does not work like this, so there is a simultaneous influence on the result, which is both hardware AND software.


Your Limits have no Limits, and this is not a contradiction.
 
doronshadmi said:
...

http://www.internationalskeptics.com/forums/showpost.php?p=4943317&postcount=5457 and http://www.internationalskeptics.com/forums/showpost.php?p=4943317&postcount=5457 are beyond your Limits.
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A hint of Moral One-upmanship
If people disagree with you, accuse them of ... narrowness or conventional thinking ...
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A dash of Be dismissive
Go on, don't hesitate. Brush people off, especially if they know about something you don't know about. ...
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And a pinch of the ever-popular Repetition
If your ideas are weak, if you have neither logic nor evidence to back them up, simply keep asserting them over and over and over again. This will convince everyone that they must be true. If they were not true, surely we wouldn't keep hearing about them all the time?
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|N| > any N member, where N={1,2,3,…}.

By following the same principle |K| > any K member, where K={|N|,1,2,3,…}.

A question:

Does |K| > |N| OR |K| = |N|?


Answer 1:

|K| > |N| by 1 (but then |N| = |{|N|,1,2,3,…}| , is false)


Answer 2:

|K| = |N| but then the whole idea of transfinite cardinals has nothing to do with extension of finite cardinals, and in particular we can't use an expression like "|N| > any N member, where N={1,2,3,…}" in order to define |N|, in the first place.

So |K| = |N| is based on the ability to define a 1-1 mapping between distinct K and N members, no matter what magnitude (finite or not) each member has.

So the whole idea of transfinite cardinals has nothing to do with magnitudes, and it is simply based on the concept of Distinction.


Please air your view on this rough idea.
 
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doronshadmi said:
|N| > any N member, where N={1,2,3,…}.
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Ok.
By following the same principle |K| > any K member, where K={|N|,1,2,3,…}.
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Nope.

A question:

Does |K| > |N| OR |K| = |N|?
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The latter.

Answer 1:

|K| > |N| by 1 (but then |N| = |{|N|,1,2,3,…}| , is false)

Answer 2:

|K| = |N| but then the whole idea of transfinite cardinals has nothing to do with extension of finite cardinals, and in particular we can't use an expression like "|N| > any N member, where N={1,2,3,…}" in order to define |N|, in the first place.
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Why would anyone use such an expression to define |N|?

So |K| = |N| is based on the ability to define a 1-1 mapping between distinct K and N members, no matter what magnitude (finite or not) each member has.
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And sure enough, there are 1-1 mappings between the members of set K and set N.

So the whole idea of transfinite cardinals has nothing to do with magnitudes, and it is simply based on the concept of Distinction.
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Nope.

Please air your view on this rough idea.
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Done.
 
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doronshadmi said:
You, jsfisher.
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Got any evidence I ever did such a thing? Didn't think so.

Got any evidence any standard mathematics text did such a thing? Didn't think so.


ETA: Maybe it is that word, define. You seem to have trouble with that word. Is that the problem? Define?
 
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Little 10 Toes said:
Doronshadmi, notice that you used the expression to define |N| and then jsfisher quoted you using it. Do you need glasses to see the different shades of gray that you post displays when things are double quoted?
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More to the point, when Doron wrote this:

doronshadmi said:
|N| > any N member, where N={1,2,3,…}
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at the beginning of his post, it was not a definition of |N|, just like 5 > 3 is not a definition for the number 5.
 
jsfisher said:
More to the point, when Doron wrote this:



at the beginning of his post, it was not a definition of |N|, just like 5 > 3 is not a definition for the number 5.
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Nonsense, |N| > any member of N={1,2,3,...} is exactly the definition of the smallest transfinite cardinal.

5 > 3 is between two finite cardinals, and therefore it is not a definition of 5.

This is defiantly not the cace with |N| definition.
 
doronshadmi said:
Nonsense, |N| > any member of N={1,2,3,...} is exactly the definition of the smallest transfinite cardinal.
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Doron, you really, really need to spend some time learning the meaning of some really, really simple terms. Definition is one such term. The above is nothing more than a simple mathematical statement. A true statement, by the way.
 
doronshadmi said:
Nonsense, |N| > any member of N={1,2,3,...} is exactly the definition of the smallest transfinite cardinal.

5 > 3 is between two finite cardinals, and therefore it is not a definition of 5.

This is defiantly not the cace with |N| definition.
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I agree with jsfisher on this one. You have only done a statement. Here, I'll do one too!

|F| > any member of F={..., -3, -2, -1}

Same, same only different.
 
Little 10 Toes said:
I agree with jsfisher on this one. You have only done a statement. Here, I'll do one too!

|F| > any member of F={..., -3, -2, -1}

Same, same only different.
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As do I.

Let's try a different tact

My cat has four legs.

A true statement.

Does having four legs define my cat?

At least in part, but my neighbor’s dog also has four legs and certainly is not my cat. Having four legs is just a property of my cat as well as my neighbor’s dog.

Does my cat define the property of having four legs?

No, not at all it is simply a property my cat and my neighbor’s dog both might share. To define the property of having four legs one would first need to define what does or does not constitute a leg and what does or does not constitute having a leg. Only then can one determine if my cat or my neighbor’s dog both meet the required definition of having four legs.


In the statement “|N| > any member of N={1, 2, 3, …}” or “|F| > any member of F={..., -3, -2, -1}” the definitions of the sets N and F are given, but the definition of the property of |N| or |F| (cardinality of those sets) is not, only the condition that it is greater then any member of the defined set is given. In the case of the set F, 0 is > any member of F={..., -3, -2, -1}, yet 0 is not |F|. In the case of the set N the cardinality of the set of all real numbers R thus |R| is > any member of N={1, 2, 3, …}, yet again |R| is not |N| by the definition of cardinality. Since |R| meets the given requirements of “> any member of N={1, 2, 3, …}” then |R| must meet the “definition of the smallest transfinite cardinal” and |R| = |N| by Doron’s given requirements.
 
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