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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
1 year, 8 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 - 1 year, 8 months ago

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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 - 1 year, 8 months ago

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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 - 1 year, 8 months ago

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