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 dissimilar to, and I might even say in principle the same as, my method described above of introducing transfinite 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.
Georg CantorRelated topics
above actual best certain defining definite fact fall former infinite innermost irrational latter might method numbers opinion principle say sense stand transfiniteRelated quotes
On this question of principle, while actual suffering was yet afar off, they the Colonies raised their flag against a power to which, for purposes of foreign conquest and subjugation, Rome in the height of her glory is not to be compared,a power which has dotted over the surface of the whole globe with her possessions and military posts, whose morning drum-beat, following the sun, and keeping company with the hours, circles the earth with one continuous and unbroken strain of the martial airs of England.
Daniel Webster
Now, if the principle of toleration were once admitted into classical education --if it were admitted that the great object is to read and enjoy a language, and the stress of the teaching were placed on the few things absolutely essential to this result, if the tortoise were allowed time to creep, and the bird permitted to fly, and the fish to swim, towards the enchanted and divine sources of Helicon --all might in their own way arrive there, and rejoice in its flowers, its beauty, and its coolness.
Harriet Beecher Stowe
Remembering that I'll be dead soon is the most important tool I've ever encountered to help me make the big choices in life. Because almost everything - all external expectations, all pride, all fear of embarrassment or failure - these things just fall away in the face of death, leaving only what is truly important. Remembering that you are going to die is the best way I know to avoid the trap of thinking you have something to lose. You are already naked. There is no reason not to follow your heart.
Steve Jobs
Peter, in showing that the Church is one and that only those who are in the Church can be saved, said: "In the Ark of Noah certain persons, numbering only eight, were saved by water, which Baptism effects in like manner for you" (1 Peter 3:20). He proves and demonstrates that the solitary Ark of Noah was the figure of the One Church. If, at the time of this Baptism of the world anyone could have been saved without having been in the Ark of Noah, then he who is outside the Church could now be brought to life by Baptism.
Cyprian
Yours of yesterday is this instant come to hand & I have but a few minutes to answer it. I am sorry that your situation obliges you to listen to propositions of the nature you describe. My opinion is that a reservation of a right to withdraw if amendments be not decided on under the form of the Constitution within a certain time, is a conditional ratification, that it does not make N. York a member of the New Union, and consequently that she could not be received on that plan. Compacts must be reciprocal, this principle would not in such a case be preserved.
James Madison
