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> Does NaN have an "order" in the set of reals or integers or whatever?

By definition, something that is not a number (real, integer, etc.) cannot be compared to something that is a number.

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It depends on what space you're working on (e.g. the https://en.wikipedia.org/wiki/Extended_real_number_line define an order on the real field union {-∞, +∞}).

Yes, but in that context, ∞ is a number. We often interpret "NaN" to mean "infinity," but it only means "not a number." Maybe I'm being pedantic, but if we want a token representing infinity as a number, it ought not be called "not a number."

IEEE754 has both infinity and NaN. They are different. NaN is always the result of an invalid operation, such as trying to take the square root of a negative number. Infinity is for when the result would be valid, but is too large in magnitude to represent. There is both positive and negative infinity.

typeof NaN

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