Both min and max should return NaN, if any of their parameters is NaN. Sorting can be defined where to place the NaNs (head/tail) but it's largely irrelevant in this case as simply the substitution won't be permitted by any compiler.

NaN is part of IEEE754 but of course it's not a 'real' number (integer numbers don't have NaNs)

Edit: you can consider NaN (and to a degree both infinities) as an exception, once it occurs - it has to be propagated. Any operation involving NaN should be returning NaN, any operation comparing NaN to anything has to return 'false'. That includes "if (NaN == NaN)". boolean isNaN(double d) is effectively "return d != d;"

> Both min and max should return NaN, if any of their parameters is NaN.

That's not a given, though. IEEE 754-2008 defined min and max as returning the non-NaN parameter. They have been removed in IEEE 754-2019 though.

The reference to IEEE 754 is made later on, mostly to answer the question posted. I meant regular functions in C alike languages - Math.min/max - java/javascript, fmin/fmax - C++. They do the "right" thing to propagate the NaN

No, the only valid result for NaN is NaN. Saturating range bounds are for real numbers.

No, it breaks the ordering requirements. NaN compares greater than and less than every number.

You can say that a call to max should return NaN if any argument is NaN, but you can't say the same about sorting. (For one thing... sorting an array doesn't return a scalar value.) Sorting is done with comparisons, and what happens if a NaN gets into the list of values will depend on which specific comparisons happen to be done.

The only reason I know what to expect is because Suckerpinch on YouTube made a video in which he managed to define a logic system using NaN and +∞, and does so by abusing min and max, among other expressions:

https://youtu.be/5TFDG-y-EHs

> 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.

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