86. Infinite extension ought to be the greatest of all extensions, but there is no such extension. From any given extension God can take away a certain quantity; for example, a yard: in that case the infinite extension would become finite, for it would be less than the first; and as the difference between the two extensions is only a yard, it is clear that not even the first could be infinite; for it is impossible that there should be only the difference of one yard between the finite and the infinite. This difficulty merits a serious consideration: at first sight it seems so conclusive that no possibility of a satisfactory solution is conceivable. The proposition that the difference between the finite and the infinite cannot be finite, is not wholly correct. We must first of all take notice that the difference between two quantities, whether finite or infinite, cannot be absolutely infinite, in the sense of diminution. Difference is the excess of one quantity over another, and necessity implies a limit; for as the excess only is considered, the quantity exceeded is not contained in the difference. Calling the difference D, the greater quantity A, and the smaller _a_, I say that D can in no hypothesis be infinite. By the supposition D = A - _a_; therefore D + _a_ = A; in order that D may equal A it is necessary to add to it _a_; therefore D cannot be infinite. If we suppose A = ∞, we shall have D = A - _a_ = ∞ - _a_, or D + _a_ = ∞. Therefore to make D infinite we must add to it _a_, and we can never have D = ∞ unless _a_ = 0; but in that case there would be no true difference, since the equation, D = A - _a_, would be converted into D = A - 0 = A, and the difference would not be real but imaginary. It follows from this that no difference between two positive quantities can be absolutely infinite; if it is so in some sense, it is not so in the sense of diminution; and the union of these two ideas of difference and infinity results in a contradiction.[40] [40] I am speaking of the difference between _positive_ quantities; for with regard to other quantities we may express an infinite difference algebraically. Let the two quantities be (∞ - _a_) and (-_a_). The difference between them will be expressed in this equation, D=(∞ - _a_) - (-_a_) = ∞ - a + a = ∞.