Cont: Deeper than primes - Continuation 2

[jsfisher]

Nope, you still don't get it. SO. WHAT? In what way does this alleged lack of awareness cause detriment to anything? What is the disadvantage?

So what?!!!? Man, haven't you been paying attention? Why, the very foundations of Mathematics have been destroyed. We now know that 0.25 and 1/4 are different numbers. We now know that 2 may or may not be in the set containing 2 as an element. We now know that the Axiom of Infinity is false (quite odd for axioms, really).

Ok, and if you are looking for practical applications, you should be aware your bank is cheating you big time. Your money can be IN the bank AND NOT-IN the bank; the bank insists it must be one XOR the other.

Oh, and most importantly, anything can be made true if you simply imagine it to be so.

 

[Worm]

So what?!!!? Man, haven't you been paying attention? Why, the very foundations of Mathematics have been destroyed. We now know that 0.25 and 1/4 are different numbers. We now know that 2 may or may not be in the set containing 2 as an element. We now know that the Axiom of Infinity is false (quite odd for axioms, really).

Ok, and if you are looking for practical applications, you should be aware your bank is cheating you big time. Your money can be IN the bank AND NOT-IN the bank; the bank insists it must be one XOR the other.

Oh, and most importantly, anything can be made true if you simply imagine it to be so.

Sadly, this is about a clear an explanation as we're ever likely to get. Too clear in fact. jsfisher is dangerously close to actual insight.

 

[doronshadmi]

In what way does this alleged lack of awareness cause detriment to anything? What is the disadvantage?

The disadvantage of the illusion that infinite collection is measured by fixed size, which blocks the real nature of actual infinity, which is beyond the domain of collections.

 

[doronshadmi]

Why, the very foundations of Mathematics have been destroyed

Exactly because mainstream mathematicians are unaware of the logical fact that the notion of collections is weaker than (is inaccessible to) actual infinity.

 

[doronshadmi]

Are we back to your inability to deal with a set without enumerating every member of it?

No, we are still stand in your inability to deal with the logical fact that no collection is accessible to actual infinity, and this logical fact is achieved without enumerating every member of any given collection.

Endlessly growing is exactly the inability of infinite collections to be measured by fixed values, and as a result they are inaccessible to actual infinity (which, in this case, is symbolized as ℵ₀).

 

[jsfisher]

Exactly because mainstream mathematicians are unaware of the logical fact that the notion of collections is weaker than (is inaccessible to) actual infinity.

Your posting history is evidence your usage of those two words, separately and together, is non-standard.

 

[doronshadmi]

Your posting history is evidence your usage of those two words, separately and together, is non-standard.

I agree with you because I show that the standard view of the considered subject, has no logical basis.

 

[doronshadmi]

We now know that 2 may or may not be in the set containing 2 as an element.

Can't deal with http://www.internationalskeptics.com/forums/showpost.php?p=12240157&postcount=2964.

 

[doronshadmi]

We now know that 0.25 and 1/4 are different numbers.

If structure (and not just value) is also considered in case of numbers, then, for example, 0.01₂ and 0.25₁₀ do not have the same structure (they are structurally different) as clearly seen in

[qimg]https://c1.staticflickr.com/7/6123/5968116238_e17a4e6f90_b.jpg[/qimg]

By your reasoning structure is ignored.

By my reasoning one can choose to ignore structure, or not.

 

[jsfisher]

Can't deal with http://www.internationalskeptics.com/forums/showpost.php?p=12240157&postcount=2964.

There is nothing there to deal with. You imagine things to be true, and assume they must be true because you imagined them as such.

As a modest recent example, you reasserted just a few posts up that in your "unbounded (endlessly growing) 2-valued logical tree" all of its branches can be encoded to represent the set of natural numbers. You imagined this to be true, and therefore it must be...except it isn't.

 

[doronshadmi]

We now know that the Axiom of Infinity is false

No, it is not false, it defines an endlessly growing collection, which is logically inaccessible to actual infinity.

 

[doronshadmi]

As a modest recent example, you reasserted just a few posts up that in your "unbounded (endlessly growing) 2-valued logical tree" all of its branches can be encoded to represent the set of natural numbers. You imagined this to be true, and therefore it must be...except it isn't.

Logically there is no such thing like "all of its branches", in case of an unbounded (endlessly growing) 2-valued logical tree.

This is a modest current example that nigher your imagination nor your reasoning actually follow my arguments.

 

[doronshadmi]

There is nothing there to deal with.

Yes, there is: the artificial restriction of membership 1 of traditional mathematics.

 

[zooterkin]

Are we back to your inability to deal with a set without enumerating every member of it?

Logically there is no such thing like "all of its branches", in case of unbounded (endlessly growing) 2-valued logical tree.

Yep.

 

[doronshadmi]

Yep.

http://www.internationalskeptics.com/forums/showpost.php?p=12330993&postcount=3005

 

[jsfisher]

Logically there is no such thing like "all of its branches", in case of an unbounded (endlessly growing) 2-valued logical tree.

That word and you are complete strangers.

This is a modest current example that nigher your imagination nor your reasoning actually follow my arguments.

I think we can all agree that neither reasoning nor vivid imagination are sufficient to follow your arguments.

 

[doronshadmi]

I think we can all agree that neither reasoning nor vivid imagination are sufficient to follow your arguments.

In your case neither reasoning nor vivid imagination is used, in order to actually follow my arguments as given in http://www.internationalskeptics.com/forums/showpost.php?p=12330799&postcount=2994 and http://www.internationalskeptics.com/forums/showpost.php?p=12330993&postcount=3005 , so?

 

[jsfisher]

In your case neither reasoning nor vivid imagination is used, in order to actually follow my arguments as given in http://www.internationalskeptics.com/forums/showpost.php?p=12330799&postcount=2994 and http://www.internationalskeptics.com/forums/showpost.php?p=12330993&postcount=3005 , so?

Referring back to your false statements, bald assertions, and circular reasoning does not advance any sort of argument.

 

[doronshadmi]

Referring back to your false statements, bald assertions, and circular reasoning does not advance any sort of argument.

It is very simple jsfisher.

NOthing (the space between { }) is logically contradiction.

YESthing (the outer "{" and "}") is logically tautology.

No collection of things (for example {a,b,c,...}) is logically contradiction or tautology.

------------

As about cardinality:

{| |} = 0

|{ }| = ∞ = the cardinality of actual infinity

{|...|} = any cardinality > 0 AND < ∞

 

[jsfisher]

It is very simple jsfisher.

NOthing (the space between { }) is logically contradiction.

The space between the braces is a space. We can use braces as a notational device in talking about sets and other things, but they have no significance beyond being an aid to communication. They certainly do not create meaning.

Also, your attempt to attribute some special meaning to a simple English word via the typographic equivalent of a pun fails. If you are hell-bent on introducing "NO thing" and "YES thing" into the terminology, go right ahead, but first you need to do something you have never done -- define them -- and if they are synonyms for existing terms, don't both, just use the existing terms.