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.

#Algebra

Easy Math Editor

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`2^{34}`	$2^{34}$
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Comments

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 - 5 years, 3 months ago

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 - 5 years, 3 months ago

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 - 5 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$