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YONG
MHajduk wrote: The fact that some numbers may not be expressed using the particular set of symbols and, at the same time, the same number may be expressed using another set of symbols is quite common and not especially interesting. MHajduk wrote: As I understood this question, revolution referred here to the definition of an indescribable number as a number impossible to describe with any set of arbitrarily chosen symbols. These symbols are all manmade. We can always create a new set of symbols to describe any numbers that are indescribable by the existing sets. Why would THAT be interesting to anyone? What is really interesting is the latest rule set by revolution: "Everything must be given in the chosen language." If we can describe the number, it is not indescribable. Yeah, I see the trick. 

14 Aug 2015, 01:43 

Tyler
revolution wrote: Whether or not Planck time is the base unit of time is not important, but I mentioned it to show that there is the possibility that time is discrete. 

14 Aug 2015, 01:44 

YONG
Tyler wrote: The idea is that orientation in space shouldn't change the outcome of an experiment ... Tyler wrote: I'm betting MHajduk could provide more detail. 

14 Aug 2015, 05:33 

Tyler
YONG wrote:
Last edited by Tyler on 14 Aug 2015, 06:54; edited 1 time in total 

14 Aug 2015, 06:06 

l_inc
revolution
Quote: But you described the process used to obtain the time period I described a process that does not uniquely identify the number. For that reason the description of the process is not a description of the number. Only the experiment is. Quote: But just the same a PI, we can describe the process to obtain PI, and just because we can't write all the digits doesn't make it indescribable I find it strange that you initiated the discussion, but do not realize that possible representations are not limited solely by digits. As long as you can specify a function able to generate arbitrary precision of the number, you can write down its complete representation as a limit of that function. Quote: I mentioned it to show that there is the possibility that time is discrete And my objection is that the term of Planck time does not indicate the time discontinuity in any way. _________________ Faith is a superposition of knowledge and fallacy 

14 Aug 2015, 14:14 

MHajduk
Answer to the YONG's question
You can watch it also in a form of presentation here: http://www.slideshare.net/fullscreen/mikhajduk/indescribablenumbers 

14 Aug 2015, 15:21 

MHajduk
Tyler wrote: I'm betting MHajduk could provide more detail. YONG wrote: I think so, too! MHajduk is an expert in theoretical physics & applied mathematics. 

14 Aug 2015, 17:40 

YONG
@MHajduk:
Thank you very much for your detailed explanation. I really like the background color of your proof, which makes it less boring to read a couple of pages that are full of text. However, I must point out that your proof does NOT address my question. My question is NOT about whether or not indescribable numbers exist, which is what your proof correctly shows. My question is about your interpretation of revolution's challenge: "As I understood this question, revolution referred here to the definition of an indescribable number as a number impossible to describe with any set of arbitrarily chosen symbols." Assume that your interpretation is correct. Here is my question for you: If we don't even know how many sets of such symbols there are and what these symbols actually represent, how could we find an example of a number that is indescribable by any sets of such symbols? See, your interpretation renders the challenge meaningless. Hope that you now understand my question. 

15 Aug 2015, 06:09 

YONG
MHajduk wrote: I'm not an expert in theoretical physics ... 

15 Aug 2015, 06:13 

MHajduk
YONG wrote: If we don't even know how many sets of such symbols there are and what these symbols actually represent, how could we find an example of a number that is indescribable by any sets of such symbols? However, that has nothing to do with describability because we assumed that an arbitrarily chosen set of symbols (alphabet) should always have a finite number of elements, so as it has been shown in my article/paper/whateverwenameit the cardinality of any available language based on such finite alphabet is much smaller than cardinality of the set of real numbers. Hence we can't "name" all real numbers, the set of "names" in any possible language (build on a base of an arbitrarily chosen finite alphabet) is too scarce to make onetoone correspondence with the set of all real numbers. The set of indescribable numbers (a subset of the set of all real numbers) behaves like "dark matter", to use the physical analogy, we know that it should exist, but we can not "catch" it with any available tool. Where do you see maninglessness? 

15 Aug 2015, 08:18 

YONG
MHajduk wrote: The set of indescribable numbers (a subset of the set of all real numbers) behaves like "dark matter", to use the physical analogy, we know that it should exist, but we can not "catch" it with any available tool. Refer to: https://en.wikipedia.org/wiki/Neutrino https://en.wikipedia.org/wiki/Hot_dark_matter MHajduk wrote: Where do you see maninglessness? Anyway, I respect your interpretation. 

15 Aug 2015, 09:56 

MHajduk
YONG wrote:
YONG wrote:


16 Aug 2015, 16:38 

revolution
Given that z is any value, show any/all values where the following is not true when using the x86 FPU for all operations (includes using the FPU for comparisons):
[1/sqrt(z)] >= 0 For simplicity assume z is limited to 32bits. If you want a slightly more challenging problem assume z is any tword (10 byte) value. 

04 Sep 2015, 05:23 

YONG
revolution wrote: Given that z is any value, show any/all values where the following is not true when using the x86 FPU for all operations (includes using the FPU for comparisons): When z is negative, "taking square root of a negative number" occurs. There could be other values that satisfy the requirement. But I have not touched FPU operations for a very long time  I am not sure. 

04 Sep 2015, 05:48 

revolution
YONG wrote: When z is zero, "division by zero" occurs. 

04 Sep 2015, 06:00 

YONG
revolution wrote:


04 Sep 2015, 06:08 

revolution
YONG wrote:
Note that the extra challenge for all 10byte values requires more forward planning than a basic brute force for all possible 80bit input values. 

24 Dec 2015, 10:07 

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