167. Although an absolutely infinite number may be indeterminately conceived, it is not susceptible of any arithmetical or geometrical expression: no series of what mathematicians call infinite expresses an absolutely infinite number.
168. The intrinsic impossibility of an actual infinite number may be demonstrated from the intrinsic repugnance of the co-existence of certain things which may be numbered.
169. The idea of the absolutely infinite real being cannot be indeterminate: it necessarily involves positive and formal perfections.
170. All that does not imply a contradiction must be affirmed of the infinite being. That which is absurd is not a perfection.
171. Analyzing indeterminate and intuitive ideas, we find that all the reality contained in them is affirmed of God.
172. The absolutely infinite being must be intelligent.
173. Intelligence is a perfection which does not imply contradiction.
174. Will and liberty must also be found in the absolutely infinite being.
175. The indeterminate idea of the infinite is favored by the combination of the ideas of being and not-being.
176. The idea of an absolutely infinite being consists in the idea of a union of all being that involves no contradiction.