Georg Cantor Quotes

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.

I realise that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.

A googolplex is precisely as far from infinity as is the number 1... no matter what number you have in mind, infinity is larger still.

The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers.

... numbers have neither substance, nor meaning, nor qualities. They are nothing but marks, and all that is in them we have put into them by the simple rule of straight succession.

Far be it from us to doubt that all number is known to Him 'Whose understanding is infinite' (Ps. 147:5). The infinity of number, though there be no numbering of infinite numbers, is yet not incomprehensible by Him Whose understanding is infinite. And thus, if everything which is comprehended is defined or made finite by the comprehension of him who knows it, then all infinity is in some ineffable way made finite to God, for it is comprehensible by His knowledge.

If half the society isn't engaged on any number of sectors, success and potential will be limited. In that sense, I do definitely believe there is a growing movement and moment for women's issues.

Many people believe that the grains of sand are infinite in multitude ... Others think that although their number is not without limit, no number can ever be named which will be greater than the number of grains of sand. But I shall try to prove to you that among the numbers which I have named there are those which exceed the number of grains in a heap of sand the size not only of the earth, but even of the universe

I think there [are] great economies that can be made starting with a round of base closings, ... I want the president to veto these pork-barrel spending bills which have grown to incredible obscene levels. I believe there are a number of weapons systems that have to be eliminated.

I believe there are 15, 747, 724, 136, 275, 002, 577, 605, 653, 961, 181, 555, 468, 044, 717, 914, 527, 116, 709, 366, 231, 425, 076, 185, 631, 031, 296 protons in the universe and the same number of electrons.

don't argue what you don't believe in. Rule number one, in law and in life.

A number of U.S. colleges are going to start having dorms for alcoholics. I believe those are called dorms.

A greater number of God's creatures believe in Mahomet's word at this hour than in any other word whatever. Are we to suppose that it was a miserable piece of spiritual legerdemain, this which so many creatures of the almighty have lived by and died by?

To excite in us tastes, odors, and sounds I believe that nothing is required in external bodies except shapes, numbers, and slow or rapid movements. ... if ears, tongues, and noses were removed, shapes and numbers and motions would remain, but not odors or tastes or sounds.

Certain sincerely devout and spiritually advanced people believe that the God of their understanding helps them find parking places and gives them advice on Mass. Lottery numbers.

From a mathematical standpoint it is possible to have infinite space. In a mathematical sense space is manifoldness, or combinations of numbers. Physical space is known as the 3-dimension system. There is the 4-dimension system, the 10-dimension system.

Of course, when you see [ musical numbers] in the movie [Out To Sea ], it's cut into a lot with other scenes, but we shot the number straight through, so here I am doing it, and sitting right in front of me in the audience was Donald O'Connor. And I was, like, "Oh, my God, I can't believe I'm performing a musical number in front of Donald O'Connor," who's one of the greats of the silver screen. But it was a thrilling experience, it really was.

I lift weights, but that's not my main focus. I'm a fighter now, and I want to evolve and make myself a well-rounded fighter, so obviously I'm not going to leave any stone unturned, when it comes to submissions, submission defense, striking, knees, leg kicks, and also learning to defend everything. It's not just an offensive sport because you're going to take some punches and you're going to give some punches. You've got to be able to handle both sides of the spectrum. I've brought in a number of highly trained trainers to help me evolve, and I believe we've left no stone unturned.

The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type.

Girls are stronger in numbers. So yes, I believe girls should stick together whenever possible.

You are quite correct in saying that I banned the export of monkeys on a humanitarian basis and not because the number was lessening... I believe in preventing cruelty to all living beings in any form.

There are reasons, increasing in number and quality, to believe that the masses of ordinary galaxies may have been underestimated by a factor of 10 or more.

Renormalization is just a stop-gap procedure. There must be some fundamental change in our ideas, probably a change just as fundamental as the passage from Bohr's orbit theory to quantum mechanics. When you get a number turning out to be infinite which ought to be finite, you should admit that there is something wrong with your equations, and not hope that you can get a good theory just by doctoring up that number.

If I remember correctly, the most efficient campaign in modern times, in terms of burn rate, had been Obama's 2012 reelect, which I believe the number was they spent 37 cents at every dollar.