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This question already has an answer here:

We've defined the square root of -1 as an imaginary number i (or j, if you're a physicist).

Is there any reason why we can't/haven't made other systems of imaginary numbers for other "impossible" operations, like log base 1 or dividing by zero?

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marked as duplicate by Hans Lundmark, Zev Chonoles, Chappers, Micah, Lucian Apr 28 '15 at 22:15

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  • $\begingroup$ Note the $\log_1$ question is kind of the same as the other question by the change of base formula. $\endgroup$ – jgon Apr 28 '15 at 22:05
  • $\begingroup$ en.wikipedia.org/wiki/Split-complex_number , en.wikipedia.org/wiki/Quaternion , and so on. $\endgroup$ – Chappers Apr 28 '15 at 22:08
  • $\begingroup$ I find most physicists I encounter use i, its nearly every electrical engineer I meet that typically uses j. Not that we aren'r aware of the use of j...we would mix it up with generalized currents which we normally use j for $\endgroup$ – Triatticus Apr 28 '15 at 22:15
  • $\begingroup$ It is, imho, mostly a practical question. You can define anything you like and we do all the time (e.g we write "Let x be..."). Something gets a name or a letter if it is useful. Pi is useful, Euler's e is useful and so are complex numbers. If tomorrow you'll find a constant or a concept that is useful or practical it will get a life of its own and maybe even its own letter.... $\endgroup$ – DannyDan Apr 28 '15 at 22:21

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