Cont: Deeper than primes - Continuation 2

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doronshadmi said:
I do not presume anything.
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You presumed several things, all irrelevant to the case at hand.

I clearly claim that your fixed-only value notion, prevents from you to grasp the notion of a2 and c2 as totally smooth and endless increasing (potential infinities) values of the Pythagorean Theorem.
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See? There you presume again. And again, what you imagine I believe or don't believe is not relevant to what you need to show.

You continue to use the Pythagorean Theorem in a realm in which it does not apply. You should focus on providing a proof that it can be extended to cover your as yet undefined triangle concept. What you fantasize about me and what you believe to be my ideas matters not at all.
 
jsfisher said:
You should focus on providing a proof that it can be extended to cover your as yet undefined triangle concept.
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jsfisher, you are saying that I "should focus on providing a proof that it can be extended to cover" my "yet undefined triangle concept".

You are totally blind to http://www.internationalskeptics.com/forums/showpost.php?p=12128672&postcount=2820, exactly because your fundamental notions of mathematics are based of fixed-only values, and you get infinity only in terms of actual infinity in terms of collections.

Mathematics (or any other subject) is leaned and understood according to one's abilities to use his\her brain skills.

So, you are an important factor of your abilities to understand my definitions, which are based both on the visual_spatial AND verbal_symbolic brain skills (which is something that you don't do, since all your mathematical notions are based on your verbal_symbolic brain skills).

Here are some concrete examples:
jsfisher said:
doronshami said:
Let a2 be infinite and let b2 be finite and > 0.
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Then it wouldn't be a triangle in an Euclidean plane, now would it.
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Why are you claiming that?

jsfisher said:
You made other errors, too
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Why you do not support your claim in details?
 
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doronshadmi said:
jsfisher, you are saying that I "should focus on providing a proof that it can be extended to cover" my "yet undefined triangle concept".
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Yes, and I have said it multiple times. Pretty basic stuff, too. A certain theorem covers a certain domain. There are several proofs available to show it is a theorem covering that domain. You want to use this certain theorem in a different domain, one not covered by the proofs.

To do that, you need to carefully define what you mean by this different domain and then prove the theorem covers it.

Do that, then you are free to use the theorem in this different domain. Without that, you have no basis.
 
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jsfisher said:
You want to use this certain theorem in a different domain, one not covered by the proofs.
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It is exactly the same domain, covered by totally smooth endlessly increasing a2 and c2 values, in this case (the smooth version of potential infinity).

This is pretty basic stuff jsfisher, but since all your mathematical notions are based on fixed values and you wrongly understand actual infinity in therms of collections, you can't understand my visual_spatial AND verbal_symbolic definitions of potential infinity (whether they are smooth or discrete) as very simply given in http://www.internationalskeptics.com/forums/showpost.php?p=12128672&postcount=2820.

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And of course you ignore my questions to you, because you have no answers as a person that uses only his verbal_symbolic brain skills, in order to do math.

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In case that you are still missing it, we are dealing here with one and only one domain, known by the name Mathematics, which is an organic whole and yet incomplete, like any healthy developing organism, which we are an essential aspect of it.
 
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doronshadmi said:
It is exactly the same domain, covered by totally smooth endlessly increasing a2 and c2 values, in this case (the smooth version of potential infinity).
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You'd need to prove that. Nothing in the Pythagorean Theorem itself nor its various proofs agree with you.
 
jsfisher said:
You'd need to prove that. Nothing in the Pythagorean Theorem itself nor its various proofs agree with you.
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It is very simple jsfisher.

All you need is to use also your visual_spatial brain skills on a2 (in this case) as a totally smooth endlessly increasing value.
 
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doronshadmi said:
It is very simple jsfisher.

All you need is to use also your visual_spatial brain skills on a2 (in this case) as a totally smooth endlessly increasing value.
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That would be after first step. You need to get the first step, well, first.
 
Hevneren said:
Seems someone got a new toy for Christmas. A totally smooth one. I think it's the same as "non-composed", but he apparently got bored with that.
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Totally smooth and non-composed are the same toy.

It seems that you don't know how to play with it, no matter what name is given to it, simply because (like jsfisher) you do not use also your visual_spatial brain skills in order to do Math.

(b.t.w please look at https://math.stackexchange.com/questions/50607/definition-of-definition in order to realize how people "understand" definition only by their verbal_symbolic brain skills).
 
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jsfisher said:
That would put you back to proof by assumption. That's not a valid proof method.
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That is an invalid assumption of one that refuses to use his visual_spatial brain skills in addition to his verbal_symbolic brain skills, in case of a2 .
 
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So try this but instead of fixed 2b, 2b is a totally smooth endlessly increasing value.
 
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doronshadmi said:
So try this but instead of fixed 2b, 2b is a totally smooth endlessly increasing value.
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Are you suggesting the linked proofs for the theorem work with your "totally smooth endlessly increasing values"? You need to show your work. A diagram might help; you so love diagrams. You will also need to show how you would extend basic arithmetic to include totally smooth endlessly increasing values.
 
jsfisher said:
Are you suggesting the linked proofs for the theorem work with your "totally smooth endlessly increasing values"? You need to show your work. A diagram might help; you so love diagrams. You will also need to show how you would extend basic arithmetic to include totally smooth endlessly increasing values.
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Also see this, where |x1-x2| is a totally smooth endlessly increasing value.

In both cases we are dealing with totally smooth endlessly increasing triangle(s), where one of the perpendicular sides has a fixed value > 0.

Now, here is my agument again, but this time, jsfisher, also use your visual_spatial brain skills.

If you do that, maybe there is a chance that you will also understand the discrete aspect of potential infinity, as given here.
 
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jsfisher said:
Use whatever reference you like...just show your work (and that other stuff I mentioned, too).
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jsfisher, in order to see my work you have no choice but to use also your visual_spatial brain skills in addition to your verbal_symbolic brain skills.

Without it you have no chance to understand potential infinity as a whole and yet incomplete (whether it is smooth or not), and also you have no chance to understand that actual infinity is both whole AND complete and therefore can't be defined in terms of multiplicity (in terms of collections, if you will).
 
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doronshadmi said:
jsfisher, in order to see my work you have no choice but to use also your visual_spatial brain skills in addition to your verbal_symbolic brain skills.
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You haven't shown any work, yet. Just assertions and hand-waving.
 
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