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Cont: Deeper than primes - Continuation 2

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doronshadmi said:
If you ignore, for example, http://www.internationalskeptics.com/forums/showpost.php?p=11706920&postcount=2438.
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In which you say a lot about the symbols used to denote empty sets. You seem to think that the braces are a tautology and the void between them is a contradiction. But a tautology is actually a formula that's always true, and a contradiction is an unsatisfiable statement. None of them are braces or voids. And nothing of this says anything at all about the Archimedean property.
 
Hevneren said:
But a tautology is actually a formula that's always true, and a contradiction is an unsatisfiable statement.
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Once again you restrict reasoning by using only your verbal-symbolic brain skills.

http://www.internationalskeptics.com/forums/showpost.php?p=11706920&postcount=2438 is based on visual-spacial AND verbal-symbolic brain skills, which are actually "two sides of the same coin" that if are used together, they actually enable to understand "the coin" and how it is actually expressed both visually AND symbolically in real life.
 
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doronshadmi said:
It is a property that disallows the endless larger and the endless smaller.
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It doesn't allow or disallow anything. It is simply a property--somethings have the property and other things don't.

The set of real numbers happens to have it.
 
CriticalThanking said:
Where did I object? Failing to honestly address criticisms posted by others is exactly remaining hidden.
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Your claim that I "Failing to honestly address criticisms posted by others" is exactly an objection of yours on my work that is based on "criticisms posted by others".

Instead of simply directly address your objection of my work by using your own arguments in details about my work, you are using "criticisms posted by others" as agents of your objection.

Again, objection by using criticisms posted by others, is exactly non-honestly remaining hidden.
 
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jsfisher said:
The set of real numbers happens to have it.
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Since no infinite collection has it, so is the case about real numbers.

"happens to have it" is exactly the illusory result of using verbal-symbolic-only brain skills in order to define the real numbers.
 
doronshadmi said:
Since no infinite collection has it, so is the case about real numbers.
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Really? Then there must be a pair of positive real numbers, A and B, for which no integer n satisfies the relation nA > B.

Now, I would have thought for any two positive reals, n = 1+floor(B/A) would work, but you must know of a pair for A and B where it doesn't (for that or any n).

What pair of reals would that be?
 
In order to be clear about my arguments about traditional mathematics, I claim that it is mostly done by persons that believe that mathematical objects are platonic, which means that they are independent of our brain-skills.

In this case we can ask, how can we deduce about these platonic things, in the first place?

My answer is that our brain is essentially inseparable of reality, yet easily can become unaware of this inseparability by partially using its skills.

In order to be aware of this failure The Axiom Of Mathematics is:

Given X (reality) no sub-X (partial expression of X), is X (reality).
 
doronshadmi said:
Since no infinite collection has it, so is the case about real numbers.
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In that case, there must exists at least one real number x for which there is no larger natural number. This follows from the definition of the Archimedean property. Please tell us the value of x.
 
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Hevneren said:
In that case, there must exists at least one real number x for which there is no larger natural number. This follows from the definition of the Archimedean property. Please tell us the value of x.
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You still try to understand the endless larger or the endless smaller in terms of fixed values.
 
doronshadmi said:
Once again you are using finitely many things in order to define infinitely many things.
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No, I did no such thing. I didn't attempt to define infinitely many anything.

The meaning of "Archimedean Property" is simple and precise, and it was only to that meaning that I referred.

Now, back to the subject: For which pair of positive reals does the set of real numbers fail to have the Archimedean Property?
 
doronshadmi said:
You still try to understand the endless larger or the endless smaller in terms of fixed values.
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No, I'm trying to understand what you're saying. Care to elaborate? What's x? Does it exist or not? I know you think that my reasoning is of the wrong kind, so please skip the part where you tell me that.
 
doronshadmi said:
My argument about Archimedean Property is exactly about infinitely many things.
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There is nothing in the Archimedean Property that cares whether a set is finite or infinite.

Your argument isn't about the Archimedean Property at all, otherwise you'd be expressing your argument in terms of how it is defined. Your argument is with the Archimedean Property, or more correctly how you misunderstand it.

You continue to fight definitions.
 
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