I think, therefore, that we ought to take great numbers of hoplites, both from Athens and from our allies, and not merely from our subjects, but also any we may be able to get for love or money in the Peloponnesus, and great numbers also of archers and slingers, to oppose the Sicilian horse.
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Book VI, 6.22-Thucydides
Pythagoras, as everyone knows, said that "all things are numbers." This statement, interpreted in a modern way, is logical nonsense, but what he meant was not exactly nonsense. He discovered the importance of numbers in music and the connection which he established between music and arithmetic survives in the mathematical terms "harmonic mean" and "harmonic progression." He thought of numbers as shapes, as they appear on dice or playing cards. We still speak of squares or cubes of numbers, which are terms that we owe to him. He also spoke of oblong numbers, triangular numbers, pyramidal numbers, and so on. These were the numbers of pebbles (or as we would more naturally say, shot) required to make the shapes in question.
Pythagoras
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 Cantor
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
I do not agree with a big way of doing things. What matters is the individual. If we wait till we get numbers, then we will be lost in the numbers and we will never be able to show that love and respect for the person.
Agnes Gonxha (Mother Teresa) Bojaxhi
I do not agree with a big way of doing things. What matters is the individual. If we wait till we get numbers, then we will be lost in the numbers and we will never be able to show that love and respect for the person.
Mother Teresa (Agnes Gonxha Bojaxhi)
Thucydides
Thunders, Johnny
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