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> a = "nan"; a = tonumber(a);
> b = "nan"; b = tonumber(b)
> print (c);
> c = a<=b;

In *some* implementations, "a" would get a true NaN, and "c" would be zero
(NaNs are not comparable to each other) but in general, "a" would be nil and
"c" would be 1, as you found out.
--lhf