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About pengkuan

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  • Birthday 11/25/1959

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  1. We analyze the mathematical mechanism that slows the time of the traveler in the twin paradox and explain what distinguishes the traveler's frame from the Earth's frame Please read the article at https://www.scienceforums.net/applications/core/interface/file/attachment.php?id=18516 PDF: Twin paradox when Earth is the moving frame url removed or Word: https://www.academia.edu/39216040/Twin_paradox_when_Earth_is_the_moving_frame
  2. Thanks Thanks I just want to know the name of this philosophy.
  3. I agree with what you say. Is it a school of thought in mathematics? Are there many people who think like you ?
  4. I know that this is the well accepted theory. But it would be great if the contrary could be proven. Yes, that is impossible. But one can always think otherwise.
  5. I do not think that a line is a set of points just because points cannot be fill all holes. But this is another story. I agree that real numbers are countable.
  6. I will change my theory to handle infinity.
  7. No. Length is the number of member of a series. So, it is a natural number.
  8. It seems that everyone thinks that natural numbers have finite values while the entire set in infinite. I'm OK with that. But in this case, the length of the set of all even numbers is finite, because it's a natural number. Actually, one cannot pass from a finite number, the length of a finite set, to infinite number, the length of a infinite set, which is the finite set when its length is stretched to infinity. Actually, if the price is 1111....., you can double it, 2*1111...=2222... Thanks for your help. I think within the set of natural number, the ordinal numbers are natural numbers.
  9. I mean that because you say “i can be an arbitrarily large finite number.”, i and j cannot be infinitely big, for example, a number with infinitely many digits like 9517452…… or \(10^{\infty }\). In this case, can we write the set of natural numbers as {1,2,3,…,n-1,n}, with n being a finite number with arbitrarily large value? If i had value 9517452…… , then the ratio i/1 would not have corresponding natural number.
  10. I was restating your explanation above with my words. So, in the counting of \(\mathbb{Q}\), the ratio i/j corresponds to the number n which is finite. For the ratio i/1, the number of count is: \[n=\frac{i(i+1)}{2}\] So, if n is a finite number, i is also finite. Does this mean that the number i is not allowed to go to infinity? In this case, \(\mathbb{Q}\) does not completely cover the plane \(\mathbb{N}\times \mathbb{N}\) . Can we say that \(\mathbb{Q}\) is countable only because i and j are not allowed to have infinite value?
  11. Yes, you are right. So, the set of the rationals is countable because every i/j corresponds to a finite number n in the counting order. At nth step, we stop the count. Although the set itself is infinite, all counting numbers are finite. But for the power set of N, the set of all even numbers corresponds to the infinite binary sequence 1010101010...... To reach it we cannot stop counting because this sequence is not finite. Can we say that the power set of N is not countable because the counting numbers of infinite subsets are infinite? Yes. I agree that I have difficulty in seizing the exact sense of the discussion.
  12. I'm very grateful to your help. Sorry for not replying you more.
  13. Se cannot work with this "definition". Yes, your definition is correct. But is it used to prove that a set is countable? For example the rationals are countable. This is proved by counting along the diagonals of the plane N*N. The set {1/1,2/1,1/2...} is bijected to {1,2,3...n,...}, thus is countable. Is the definition used here?
  14. Why X is infinite? If X={1,2} and Y ={1}, would X and Y fit this definition?
  15. Can we have a definition of infinite set? Without a proper definition, work on infinite set does not have sense. Se cannot work with this "definition".
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