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Zero is the neutral element of addition; a + 0 = a, for any a. Since a x 0 = 0 and -1 x a = -a, it follows that -1 x 0 = -0 (although this is often not differentiated from +0, and indeed is not commonly acepted as being different except in limits; thus -0 = +0 = 0). a + (-b) = a - b, and thus a - 0 = a + (-0) = a + 0 = a, as required by the neutral element property.

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Q: How are adding 0 and subtracting 0 the same?
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