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So you disagree with the IEEE floating point specification, then? Javascript is directly following spec there.

Do you think that such rule for NaN state is useful?

Does that spec forces you to implement equality test between floating point numbers?

...yes? I'm not sure exactly what you're asking here, though.

I'm asking if it is really a good idea for a language to provide equality/inequality for floating point numbers when it's often mistake to do that.

So disallow the direct operator but allow equality to be deduced indirectly by usage of > < >= <= ?