Incomparable abominations

Paul Moore gustav at
Sun Mar 23 21:28:27 CET 2003

mertz at (David Mertz, Ph.D.) writes:

> Even then, no matter how you cut it, the relation "1j < 2j" is
> self-evident and natural.

Indeed. It's self-evidently undefined.

> How can I explain to anyone why that is an error rather than a True
> result?!

You start by explaining what 1j and 2j mean. Once you've done that
(and if you've done it properly, you've covered the fact that there is
no defined ordering on the complex numbers), it's self-evident.

Anyone who doesn't understand the properties of complex numbers
doesn't have much justification for using them. Many people who do
understand them probably *still* don't have a need to use them in

But having said all this, I think you have a point that people can
(not all do, though) have different intuitions about sorting and
comparison operations - probably because when sorting "real world"
items (books on shelves for example) we don't explicitly think in
terms of comparisons. But I'm not sure it's possible to formalise such
a distinction in a way which is implementable, or of practical use in
a computer program.

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