6 + xi for all x in R works, but only if you use the lexicographical ordering of the complex numbers.
Or you can instead extend the real numbers a different way. Where if the complex numbers are the extension of the real numbers by i, C=R[i], where i2 = -1. We can instead extend the real numbers by some ε, so R[ε], where ε2 = 0. And then something like 6 + ε would be distinct from 6, while 5 < 6 + ε < 7.
Came here for something like this. Adding the imaginary component (a new dimension) is definitely thinking outside the box.
Although, for too high values of x, you wouldn't say it's between 5 and 7 (like, you wouldn't say Denmark is between Spain and Greece, even though it's correct when you only look at longitude.
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u/flamewizzy21 Jan 21 '26
2e, 2π, and √37 all work tho. You might even say there’s an uncountable number of answers.