Rule and Exception
-
Statement 1: Every rule has an exception. Statement 2: Statement 1 is a rule. Therefore Statement 1 has an exception. Conclusion: There is at least one rule which has no exception. Would you agree with this conclusion? If so, is there any example of a rule having no exception?
-
Statement 1: Every rule has an exception. Statement 2: Statement 1 is a rule. Therefore Statement 1 has an exception. Conclusion: There is at least one rule which has no exception. Would you agree with this conclusion? If so, is there any example of a rule having no exception?
Friends don't let friends program in Basic.
If you can't find time to do it right the first time, how are you going to find time to do it again? PartsBin an Electronics Part Organizer - Release Version 1.4.0 (Many new features) JaxCoder.com Latest Article: EventAggregator
-
Statement 1: Every rule has an exception. Statement 2: Statement 1 is a rule. Therefore Statement 1 has an exception. Conclusion: There is at least one rule which has no exception. Would you agree with this conclusion? If so, is there any example of a rule having no exception?
Kurt Gödel proved a version of Statement 1: In any formal language, there are questions that can be asked but not answered. A perfect example of Gödel's incompleteness law can be found in math: - Positive Integers (lengths) can subtract a larger number from a smaller number. The answer is a negative integer, leading to: - All integers can divide and result in a fraction, leading to: - Fractions can be used in geometry to result in real numbers, leading to: - Real Numbers can have square roots that are imaginary, leading to: - Complex numbers, etc...
-
Statement 1: Every rule has an exception. Statement 2: Statement 1 is a rule. Therefore Statement 1 has an exception. Conclusion: There is at least one rule which has no exception. Would you agree with this conclusion? If so, is there any example of a rule having no exception?
I reject statement 1.
-
Statement 1: Every rule has an exception. Statement 2: Statement 1 is a rule. Therefore Statement 1 has an exception. Conclusion: There is at least one rule which has no exception. Would you agree with this conclusion? If so, is there any example of a rule having no exception?
-
Statement 1: Every rule has an exception. Statement 2: Statement 1 is a rule. Therefore Statement 1 has an exception. Conclusion: There is at least one rule which has no exception. Would you agree with this conclusion? If so, is there any example of a rule having no exception?
-
Statement 1: Every rule has an exception. Statement 2: Statement 1 is a rule. Therefore Statement 1 has an exception. Conclusion: There is at least one rule which has no exception. Would you agree with this conclusion? If so, is there any example of a rule having no exception?
A rule having no exception: "death and taxes"
The difficult we do right away... ...the impossible takes slightly longer.
-
A rule having no exception: "death and taxes"
The difficult we do right away... ...the impossible takes slightly longer.
-
Statement 1: Every rule has an exception. Statement 2: Statement 1 is a rule. Therefore Statement 1 has an exception. Conclusion: There is at least one rule which has no exception. Would you agree with this conclusion? If so, is there any example of a rule having no exception?
Amarnath S wrote:
Would you agree with this conclusion? If so, is there any example of a rule having no exception?
Agreeing that a proof is valid is not the same as stating that it must be true. Now claiming that it is true could suggest that one should provide the example. Or provide other discussions that would suggest it is true. Or just believe and dispense with the work. My favorite example with this is geometry (Euclidean) where parallel lines do not intersect. I certainly believe it. And I doubt anyone can provide an example that shows they do intersect. But for that matter they cannot provide an example where they do not intersect either.
-
Statement 1: Every rule has an exception. Statement 2: Statement 1 is a rule. Therefore Statement 1 has an exception. Conclusion: There is at least one rule which has no exception. Would you agree with this conclusion? If so, is there any example of a rule having no exception?
-
Amarnath S wrote:
Would you agree with this conclusion? If so, is there any example of a rule having no exception?
Agreeing that a proof is valid is not the same as stating that it must be true. Now claiming that it is true could suggest that one should provide the example. Or provide other discussions that would suggest it is true. Or just believe and dispense with the work. My favorite example with this is geometry (Euclidean) where parallel lines do not intersect. I certainly believe it. And I doubt anyone can provide an example that shows they do intersect. But for that matter they cannot provide an example where they do not intersect either.
jschell wrote:
parallel lines do not intersect
Though I am not a theoretical physicist, have heard that "space is curved", whatever it means. If space is curved, will there be a possibility of parallel lines meeting? Not sure.
-
In a certain village, a barber shaves all those who do not shave themselves. Who shaves the barber?
"A little song, a little dance, a little seltzer down your pants" Chuckles the clown
The famous Russel's Paradox, from what i remember.
-
Statement 1: Every rule has an exception. Statement 2: Statement 1 is a rule. Therefore Statement 1 has an exception. Conclusion: There is at least one rule which has no exception. Would you agree with this conclusion? If so, is there any example of a rule having no exception?
You : does a solution to the Russel Paradox exist ChatGPT Yes, several solutions to the Russell Paradox exist, which emerged after Bertrand Russell presented the paradox in 1901. One common solution is to restrict the comprehension principle, which states that for any property, there exists a set of all objects that have that property. By restricting this principle, mathematicians and logicians have been able to formulate set theories, like Zermelo-Fraenkel set theory (ZF) or von Neumann-Bernays-Gödel set theory (NBG), which avoid the paradox by disallowing the formation of certain "self-referential" sets. Another approach is to distinguish between sets and classes, where classes can contain sets but not be sets themselves, thereby sidestepping the contradiction. These solutions have allowed set theory to develop into a foundational framework for mathematics without succumbing to paradoxes like Russell's. Me : If Statement 2 is a rule it must have an exception. Conclusions: Statement 1 has no exception. There is at least one rule which has no exception.
-
jschell wrote:
parallel lines do not intersect
Though I am not a theoretical physicist, have heard that "space is curved", whatever it means. If space is curved, will there be a possibility of parallel lines meeting? Not sure.
Amarnath S wrote:
will there be a possibility of parallel lines meeting
Spherical geometry rather than Euclidian. But one can also start in on a definition since a line, even theoretical, could still be claimed to be something that must exist in the universe. So if the universe is curved then the line must be as well. But then what happens with the degrees in a right triangle which can only exist if those lines do not intersect.
-
Kurt Gödel proved a version of Statement 1: In any formal language, there are questions that can be asked but not answered. A perfect example of Gödel's incompleteness law can be found in math: - Positive Integers (lengths) can subtract a larger number from a smaller number. The answer is a negative integer, leading to: - All integers can divide and result in a fraction, leading to: - Fractions can be used in geometry to result in real numbers, leading to: - Real Numbers can have square roots that are imaginary, leading to: - Complex numbers, etc...
I always think of Godel’s Completeness/Incompleteness theorems when people invent new encoding systems, etc. XML : How do I encode “<“? < Well how do I encode ampersand? & etc. CSV How do you encode a comma? Enclose it in quotes. How do you encode a quote? Double it! My practical interpretation: Define a system: There will always be something outside of its boundaries! My favorite example is good old int getc(); It returns a char or -1 for EOF/End of File. EOF is outside of the char system.
-
Statement 1: Every rule has an exception. Statement 2: Statement 1 is a rule. Therefore Statement 1 has an exception. Conclusion: There is at least one rule which has no exception. Would you agree with this conclusion? If so, is there any example of a rule having no exception?
