What, however, is a + 1, or-1? Obviously nothing else than a single + or-. The figure is quite superfluous, and only indicates how often + or-has been assumed; instead, therefore, of + 1 we can posit +; instead of-1 simply-. The series + 1 + 1 + 1 is synonymous with + + +; or instead of 3 we may posit + + +, and so on for every figure ad libitum. The figures are nothing more than shorter signs for the two highest mathematical forms or ideas of numbers. Numbers are nothing different from the ideas of numbers; they are the latter themselves, only several times posited. Essentially numbers do not exist, but only their two ideas. These ideas, however, exist an infinite number of times. Multiplicity or _real_ infinity is, accordingly, nothing special or particular, but only an arbitrary repetition of the Ideal, an incessant positing of the idea. The idea posited is reality, non-posited it is = 0. 46. The first multiplicity is duality, +-. This duality alters nothing in the essence of the monas, for +-is = 0. It is the monas itself only under another form. In multiplication it is thus the form alone that changes. There are many forms, but not many essences. 47. The first or primary duality is not, however, a double unity, both members of which are of equal rank, but an antagonism, disunion, or _diversity_. Many diversities are _multiplicity_. The Many is thus complex. The first form is not therefore a simple division of zero or the primary unity, but an antagonistic positing of itself, a becoming manifold. 48. Every Finite is in the same manner only the self-definition of the Eternal. The Eternal becomes, accordingly, real, by binary self-division. When the Eternal is manifested, it is either a positive or negative. The whole of arithmetic is nothing else than a ceaseless act of positing and negating, of affirming and denying. All realization is nothing else than the act of positing and negating. The act of positing and negating of the Eternal is called realization.