49. Positing and negating is, however, an _act_ or function. Arithmetic is, therefore, a ceaseless process of acting or performing. Numbers are _acts_ of the primary idea, or, properly speaking, stationary points of its function, and hence proceeds a division into the two ideas + and -. If these remain always alone nothing is added to them. They alone produce the whole science of arithmetic, and simply because they are never exhausted by the act of positing themselves repeatedly, but capable after this of again becoming suppressed. Since + is in essence nothing else than a simple positing, a mere affirmation, and-a mere suppression of this affirmation, a negation; so is the positive unity = 1 nothing but an affirmation once declared, and the whole series of numbers is a reiterated affirmation. The act of affirmation alone gives the number, and the latter is thus the definite quantity devoid of intrinsic value. Bare affirmation alone without reference to any substance is unity, duality, &c. SOMETHING. 50. Still, however, there must be something, which is posited and negatived. The form must have a substance. This something is the primary idea, or the very Eternal of mathematics, the zero; for + - is = 0. The + is naught else than zero affirmed; the - naught else than this + 0 negatived = - 0. Now since an affirmation once declared is = 1, so are unity and zero identical. Zero differs only from finite unity in that it is not affirmed. 51. The - is not simply the want of affirmation, but its explicit abstraction. The + presupposes the 0; the - the + and 0; the 0, however, presupposes neither + nor-. Purely negative quantities are, as is known, a nonentity, because they can only bear reference to positive quantities. The - is, indeed, the retroversion of + into 0; yet alone, therefore, it is not perfectly equal to 0. It is a retrovertent, and consequently the second _act_, which presupposes the positive. By the - we know what is not; the 0 is, however, a nothing in every respect. The - is the _copula_ between 0 and +. 52. If the + is the 0 posited, so is it a nothing posited or determined. This position is, however, a number, and therefore a mathematical something. The nothing thus becomes a something, a Finite, a Real, through the simple positing of itself, and the something becomes a nothing by the removal of this self-position. The nothing itself is, however, the mere neglect of its self-position. The something, the + -, has consequently not arisen or been evolved out of nothing, or been produced from it by addition; but it is nothing itself; the whole undivided nothing has become unity. The nothing _once_ posited as nothing is = 1. We cannot speak of production or evolution in this case; but of the complete identity and uniformity of the nothing with the something; it is a virgin product or birth.