If there is some determinate succession of defined whole real numbers, among which there exists no greatest, on the basis of this second principle of generation a new number is obtained which is regarded as the limit of those numbers, i.e. is defined as the next greater number than all of them.
Georg Cantor
There is presumably an upper limit to the carrying capacity of humans on earth—of the numbers that agriculture can support—and that number is usually estimated at between 13-15 billion, though some people think the ultimate numbers might be much higher. (2001)
Niles Eldredge
The integers, the rationals, and the irrationals, taken together, make up the continuum of real numbers. It's called a continuum because the numbers are packed together along the real number line with no empty spaces between them.
Brian Hayes
That from the outset they expect or even impose all the properties of finite numbers upon the numbers in question, while on the other hand the infinite numbers, if they are to be considered in any form at all, must (in their contrast to the finite numbers) constitute an entirely new kind of number, whose nature is entirely dependent upon the nature of things and is an object of research, but not of our arbitrariness or prejudices.
Georg Cantor
Mathematics is in its development entirely free and is only bound in the self-evident respect that its concepts must both be consistent with each other, and also stand in exact relationships, ordered by definitions, to those concepts which have previously been introduced and are already at hand and established. In particular, in the introduction of new numbers, it is only obligated to give definitions of them which will bestow such a determinacy and, in certain circumstances, such a relationship to the other numbers that they can in any given instance be precisely distinguished. As soon as a number satisfies all these conditions, it can and must be regarded in mathematics as existent and real.
Georg Cantor
This annoyed me: I was on the phone with somebody today tryin to get a phone number from that person and write it down, but they didn't have phone number rhythm and that pissed me off. You know what I'm talkin about? Phone number rhythm. Especially if there's like an area code involved, like 'two one two - bum bum buh - bum buh bum buh!' That is the rhythm I think we're all familiar with. This guy had no clue! I was like "Okay, Hank. Gimme the number." He's like "Alright. It's two one two nine - fifteen eight eleven six [mumbling incoherently] fou.. tw.. five.. eight.. seven.. two." "Did you throw in your zip code? Cause I got a lot of extra numbers over here. I have extra. I can almost start a new number! What do ya got?! Start again from the top!" They really screw you up on the last four numbers. That's where they get ya. "Five five five - six.. teen forty one" "Dude, I already wrote the six! I made the dash too close, I can't shimmy the one in there now! Forget you!"
Kevin James
Cantor, Georg
Capa, Robert
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