91. Is an infinite number possible? Does the union of the idea of number with the idea of the absolute negation of limit, involve any contradiction which prevents the realization of the conception? Whatever number we may conceive, we can always conceive one still greater: this seems to show that no existing number can be absolutely infinite. If we suppose this number to be realized, an intelligence may know it, and may multiply it by two, three, or any other number; therefore the number may be increased, and consequently it is not infinite. This difficulty is far from being conclusive, if we examine it carefully. The intellectual act of which it speaks, would be impossible on the supposition of the existence of an infinite number. If the intelligence should not know the infinity of the number, it might make the multiplication, but it would fall into a contradiction through its ignorance; for the number being absolutely infinite, could not be increased; its multiplication would be an absurdity, and the intelligence making it, would combine two ideas which would still be repugnant, although not known to be so by the intelligence. If the absolute infinity of the existing number were known to the intelligence, the idea of multiplication could never be associated with it; for the intelligence would know that all possible products already exist. 92. An absolutely infinite number cannot be expressed in the algebraic or geometrical values; the attempt so to express it limits it in a certain sense, and therefore destroys its absolute infinity. If the expression ∞, represented an absolutely infinite number, it would not be susceptible of any combination which would increase it: to suppose that it may be multiplied by other numbers, finite or infinite, is to take its infinity in another than an absolute sense. The fraction a/0 does not express an infinite value in all the strictness of the word; for it is evident that whatever be the value of a/0 it will always be less than 2a/0 or, in general, less than na/0 n representing a value greater than unity. 93. Neither can an infinite number be represented in geometrical values.