I wish there were a recent remake of it.

Zero is not absence of a value. It has a value, it happens to be 0. Same for undefined/infinity. They exist.

Let the hardware engineers figure out an efficient way to deal with it. If it costs more, well if we add up all of the costs of bugs due to zero/null conversions, maybe it was worth it.

Equality comparison must be reflexive for things on which it is defined.

It is wrong to say that NaN is not equal to Nan (because a NaN is neither equal nor not equal with a NaN).

When the invalid operation exception is disabled, because the programmer is too lazy to write a SIGFPE handler or for whatever other mechanism is provided by the operating system to report hardware exceptions, then the set of floating-point numbers is extended with NaNs and the resulting extended set is no longer a totally-ordered set, but only a set on which a partial order is defined.

While floating-point number with NaNs are the best known because they are standardized, there are a lot of real sets that are best modeled as partially-ordered sets, so programming languages should have supported this and programmers should have been taught that partial order relations are something normal and natural, not something weird.

In any partially-ordered set there are elements like the NaNs, on which the relations of order and of equality may be undefined.

Thus NaN is neither equal nor not equal with NaN, but this relationship is undefined.

While for totally-ordered sets 6 relational operators are sufficient, for partially-ordered sets 14 relational operators are necessary.

When the 6 ALGOL relational operators (inherited by all later programming languages) are extended to 14, 6 new operators are provided by the negation of the 6 ALGOL operators, because in a partially-ordered set none of the 6 negations is equivalent with one of the 6 standard operators (like it happens in totally-ordered sets, where e.g. "not less" is the same as "greater or equal"). (In this statement, I considered among the 6 standard operators "less or greater", like in BASIC or SQL "<>", instead of "not equal", like in C "!=".)

The remaining 2 extra relational operators are "less or equal or greater", which could be written "<=>" or ">=<", which may be true only when no operand is a NaN, and its negation, which is equivalent with "one of the operands is a NaN".