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Curiosity on floor functions

How do you get the floor function of a complex number? Is it defined? In particular, for example, what is the value of \(\left \lfloor \frac{1}{3} + \frac{i}{2} \right \rfloor \)?

I do not know the answer to this problem. This is merely out of curiosity, no special reason for posting.

Note by Manuel Kahayon
9 months ago

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Note that since there is no order amongst the complex numbers, there is no way to find an integer s = \( [z] \) such that, \( z - 1 < s \leq z \) , that you require. Ameya Daigavane · 9 months ago

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@Ameya Daigavane Thank you! I was thinking that maybe there was some special case, but, as it turns out, finding the floor function of a complex number is, apparently, not possible. Thanks once again! Manuel Kahayon · 9 months ago

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@Manuel Kahayon No problem! The lack of an order in C means that a lot of our intuition that we've adapted for R has to change. Ameya Daigavane · 9 months ago

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