actually, they are both equal to infinity:

    #include <stdio.h>

    int main()
    {
	float a = 1. / 0;
	float b = 2. / 0;

 	printf("%f == %f ? %d\n", a, b, a == b);
        return 0;
    }

will print:

    inf == inf ? 1

Moreover:

    #include <stdio.h>

    int main()
    {
	float a = 0. / 0;
	float b = a;

 	printf("%f == %f ? %d\n", a, b, a == b);
        return 0;
    }

    nan == nan ? 0

So this is certainly surprising without knowing quite a bit already about floats, because it means = is not only not transitive but even not reflexive.

Actually no. Just in case you were confused by cdavid's sample code: the concise explanation is that division by zero in IEEE floating point produces an infinity (there are two: positive and negative), not a NaN. Neither is necessarily an "error" in the sense of a runtime exception (the generation of which is programmable).