La théorie des séries infinies en général est justqu’à présent très mal fondée. On applique aux séries infinies toutes les opérations, come si elles aient finies; mais cela est-il bien permis? Je crois que non. Où est-il démonstré qu/on ontient la différentielle dune série infinie en prenant la différentiaella de chaque terme. Rien n’est plus facile que de donner des exemples où cela n’est pas juste.
Until now the theory of infinite series in general has been very badly grounded. One applies all the operations to infinite series as if they were finite; but is that permissible? I think not. Where is it demonstrated that one obtains the differential of an infinite series by taking the differential of each term? Nothing is easier than to give instances where this is not so.

Interestingly, according to modern astronomers, space is finite. This is a very comforting thought—particularly for people who can never remember where they have left things.

It is going to be necessary that everything that happens in a finite volume of space and time would have to be analyzable with a finite number of logical operations. The present theory of physics is not that way, apparently. It allows space to go down into infinitesimal distances, wavelengths to get infinitely great, terms to be summed in infinite order, and so forth; and therefore, if this proposition [that physics is computer-simulatable] is right, physical law is wrong.

It is known that there is an infinite number of worlds, but that not every one is inhabited. Therefore, there must be a finite number of inhabited worlds. Any finite number divided by infinity is as near to nothing as makes no odds, so if every planet in the Universe has a populations of zero then the entire population of the Universe must also be zero, and any people you may actually meet from time to time are merely the products of a deranged imagination.

Our minds are finite, and yet even in these circumstances of finitude we are surrounded by possibilities that are infinite, and the purpose of human life is to grasp as much as we can out of the infinitude.

We come no nearer the infinitude of the creative power of God, if we enclose the space of its revelation within a sphere described with the radius of the Milky Way, than if we were to limit it to a ball an inch in diameter. All that is finite, whatever has limits and a definite relation to unity, is equally far removed from the infinite... Eternity is not sufficient to embrace the manifestations of the Supreme Being, if it is not combined with the infinitude of space.

We should like Nature to go no further; we should like it to be finite, like our mind; but this is to ignore the greatness and majesty of the Author of things.