Timeline for Operation between complex numbers whose answer is not complex [duplicate]
Current License: CC BY-SA 4.0
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| Oct 11, 2022 at 1:27 | comment | added | user2661923 | Index the letters of the alphabet A,B,C,...,Z as $L_0, L_1, \cdots, L_{25}.$ Construct the function $$f:\Bbb{C} \to \{A,B,\cdots,Z\}$$ as follows: For $$k \in \{0,1,2,\cdots,24\},$$ if $~k \leq |z| < (k+1),~$ then $~f(z) = L_k.~$ If $~25 \leq |z|,~$ then $~f(z) = L_{25}.$ | |
| Oct 10, 2022 at 20:22 | history | edited | user1105100 | CC BY-SA 4.0 |
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| Oct 10, 2022 at 20:20 | history | closed |
Lee Mosher CommunityBot |
Duplicate of Is there a domain "larger" than (i.e., a supserset of) the complex number domain? | |
| Oct 10, 2022 at 20:19 | history | edited | user1105100 | CC BY-SA 4.0 |
added 635 characters in body
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| Oct 10, 2022 at 20:18 | comment | added | user1105100 | @user2661923 I consider real numbers to be complex, i.e., I'm looking for an operation whose the answer is neither complex nor real (neither rational nor integer.) | |
| Oct 9, 2022 at 20:30 | comment | added | user2661923 | Example : if $z$ is any complex number of form $(x + iy) ~: ~x,y \in \Bbb{R}$, let $~\overline{z}~$ denote the complex conjugate of $z$. That is, $~\overline{z}~ = (x - iy).~$ Then, both of the following expressions are guaranteed to produce a Real number: $$[z + \overline{z}] ~~~\text{and}~~~ [z \times \overline{z}].$$ | |
| Oct 9, 2022 at 18:08 | comment | added | J.G. | Thanks for answering my question. I guess what you're hoping for is a map outside of $\Bbb C$ whose definition doesn't mention anything outside of $\Bbb C$, because $zj$ is "artificial" insofar as it has an explicit $j$ factor. | |
| Oct 9, 2022 at 18:05 | comment | added | user1105100 | @J.G. Real numbers are complex. Is it an operation "between" complex numbers? And is it not "artificial"? For quaternions I found a similar question but no answer. My question wasn't specifically with quaternions in mind. | |
| Oct 9, 2022 at 17:49 | review | Close votes | |||
| Oct 10, 2022 at 20:21 | |||||
| Oct 9, 2022 at 17:45 | comment | added | J.G. | Do you count real numbers as "not complex"? If so, take $|z|$; if not, take $zj$ with $j\in\Bbb H$, which maps $x+yi$ with $x,\,y\in\Bbb R$ to $xj+yk$, if we identify $i\in\Bbb C$ with $i\in\Bbb H$. | |
| Oct 9, 2022 at 17:39 | answer | added | Jam | timeline score: 0 | |
| Oct 9, 2022 at 17:20 | comment | added | user1105100 | Yes, I was aware of that concern. I wanted to ask if there are any "standard" operations or functions. And only defined ones, excluding $0/0$, etc. | |
| Oct 9, 2022 at 17:17 | comment | added | FShrike | Welcome. You're essentially asking for a function $f:\Bbb C\to X$ for some $X$ which is "not $\Bbb C$". Such functions are legion. That's also not a satisfying answer, I'm sure. | |
| S Oct 9, 2022 at 17:12 | review | First questions | |||
| Oct 9, 2022 at 17:28 | |||||
| S Oct 9, 2022 at 17:12 | history | asked | user1105100 | CC BY-SA 4.0 |