Timeline for Why is there never a proof that extending the reals to the complex numbers will not cause contradictions?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Nov 10, 2014 at 13:07 | comment | added | nb1 | hmm maybe, yeah. | |
| Nov 10, 2014 at 13:02 | comment | added | hmakholm left over Monica | @NikhilBellarykar: Without introducing $i$ at all, I'm not sure how one would even develop (or formulate) a desire to make complex numbers rigorous. | |
| Nov 10, 2014 at 12:55 | comment | added | nb1 | It is straightforward when one is armed with the assumption $i^2=1$, I agree. But what happens in the case when one is not? I mean, can one make this seem rigorous $and intuitive$ without introducing $i$ at all? | |
| Nov 10, 2014 at 12:33 | comment | added | hmakholm left over Monica | @NikhilBellarykar: It is pretty straightforward if you have already played around with complex numbers in the form $a+bi$ without having a rigorous background for doing so, just under the assumption $i^2=-1$. Then the intention is for the pair $(a,b)$ to represent $a+bi$, and the multiplication rule follows from expanding $(a+bi)(c+di)$ and collecting like terms. | |
| Nov 10, 2014 at 12:15 | comment | added | nb1 | While the above is rigorous enough, it is not 'intuitive' or 'straightforward' (so to speak), especially if one looks at the function $g((a,b),(c,d))$. Any reasoning as to why the function$g$ is the one given above would be helpful, because the nonspecialist will always ask- why this function and not something else. I know that the original question is only concerned with the 'non-contradiction' thing. In addition, I think some reasoning would be $nice$, that's all. | |
| Aug 14, 2013 at 14:33 | history | edited | Marc van Leeuwen | CC BY-SA 3.0 | spelling |
| Aug 11, 2013 at 10:41 | history | edited | hmakholm left over Monica | CC BY-SA 3.0 | oops, fix wrong addition :-[ |
| Aug 10, 2013 at 13:13 | vote | accept | FireGarden | ||
| Aug 10, 2013 at 13:13 | vote | accept | FireGarden | ||
| Aug 10, 2013 at 13:13 | |||||
| Aug 10, 2013 at 13:08 | history | answered | hmakholm left over Monica | CC BY-SA 3.0 |