Finite Number Quotes

However unapproachable these problems may seem to us and however helpless we stand before them, we have, nevertheless, the firm conviction that their solution must follow by a finite number of purely logical processes.

Life is not a continuous process, there's some sort of finite number of achievements that defines your life.

To make our position clearer, we may formulate it in another way. Let us call a proposition which records an actual or possible observation an experiential proposition. Then we may say that it is the mark of a genuine factual proposition, not that it should be equivalent to an experiential proposition, or any finite number of experiential propositions, but simply that some experiential propositions can be deduced from it in conjunction with certain other premises without being deducible from those other premises alone.

The first rule of economics is that there is an infinite number of desires chasing a finite number of goods, services and resources. The first rule of politics is to ignore the first rule of economics.

The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrational numbers is wholly disimilar to, and I might even say in priciple the same as, my method described above of introducing trasfinite numbers. One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite.

Definitions must contain the means of reaching a decision in a finite number off steps, and existence proofs must be conducted so that the quantity in question can be calculated with any degree of accuracy.

I haven't seen any claim that Piraha lacks recursion, that is, that there are a finite number of sentences or sentence frames. If that's so, it would mean that the speakers of this language aren't making use of a capacity that they surely have, a normal situation; plenty of people throughout history would drown if they fall into water.

In any finite region of space, matter can only arrange itself in a finite number of configurations, just as a deck of cards can be arranged in only finitely many different orders. If you shuffle the deck infinitely many times, the card orderings must necessarily repeat.

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.

Euclid manages to obtain a rigorous proof without ever dealing with infinity, by reducing the problem [of the infinitude of primes] to the study of finite numbers. This is exactly what contemporary mathematical analysis does.

What I assert and believe to have demonstrated in this and earlier works is that following the finite there is a transfinite (which one could also call the supra-finite), that is an unbounded ascending lader of definite modes, which by their nature are not finite but infinite, but which just like the finite can be determined by well-defined and distinguishable numbers.

When I was in college, for the games of that era, I was as hard core as anyone was. I wouldn't say I outgrew it, but you always have to have a finite number of addictions.

Internet TV and the move to the digital approach is quite revolutionary. TV has historically has been a broadcast medium with everybody picking from a very finite number of channels.

We each have a finite number of heartbeats, a finite amount of time. But we have enough heartbeats and enough time to do what is important.

In theory, there is nothing the computer can do that the human mind can not do. The computer merely takes a finite amount of data and performs a finite number of operations upon them. The human mind can duplicate the process