Timeline for Logic nonsense/paradox
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Sep 18, 2016 at 20:48 | history | edited | Phani Raj | CC BY-SA 3.0 | deleted 171 characters in body |
| Oct 9, 2012 at 13:58 | comment | added | MJD | Cantor's proof isn't even a proof by contradiction. It takes a given function $f:X\to \wp(X)$ and explicitly constructs an element of $\wp(X)$ that is not in the range of $f$, showing that $f$ is not surjective. | |
| Oct 9, 2012 at 13:43 | comment | added | Carl Mummert | You don't get a paradox because the bijection that was assumed to exist earlier in the proof doesn't exist, and that nonexistence is what the theorem is proving. A proof by contradiction can certainly end in a contradiction without establishing any sort of "paradox". Cantor's proof is just a proof by contradiction. | |
| Oct 9, 2012 at 13:36 | comment | added | Phani Raj | Can you explain in which way this is not paradox,Please ::At the final step you get like:: If $x\in A,$then x is not in A. If x is not in A, then x is in A. | |
| Oct 9, 2012 at 13:33 | comment | added | Carl Mummert | yes, you do get a proof by contradiction, but the result of Cantor's proof is still perfectly consistent, not paradoxical. | |
| Oct 9, 2012 at 13:30 | comment | added | Phani Raj | In Cantor's proof you get the contradiction by constructing above scenario and there by you prove the result. You can refer Analysis by Terence Tao for detailed explanation. | |
| Oct 9, 2012 at 13:03 | history | edited | MJD | CC BY-SA 3.0 | added 1 characters in body |
| Oct 9, 2012 at 12:57 | comment | added | Carl Mummert | I don't think that Cantor's proof is "paradoxical". Russell's paradox can be distinguished at least somewhat because it refers to sets, while the statement above is purely logical without any mathematical content. | |
| Oct 9, 2012 at 11:25 | history | answered | Phani Raj | CC BY-SA 3.0 |