10 MATHESIS. 



nothing else than the definition of 0. is the reduction 

 of the positive and negative series of numbers, upon 

 which the whole of arithmetic depends. A series of 

 numbers is, however, nothing else than a repetition of a 

 + 1 or a 1 ; consequently, the whole of arithmetic 

 reduces itself to + 1 1. 



What, however, is a + 1, or 1 ? Obviously nothing- 

 else than a single + or . The figure is quite super- 

 fluous, 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. Num- 

 bers 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 

 4- 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 diver- 

 sities 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, accord- 

 ingly, real, by binary self-division. When the Eternal is 



