The New Infinite And the Old Theology
The New Infinite And the Old Theology
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Let us call the bunch of these rays a bundle. It is evident that the number of rays of the bundle is the same as the number of points in the region A, one ray through each point of A, one point of A on each ray of the bundle: this number, we have seen, is the same as the number of points on the sphere ; and this, again, the same as the number of rays of the entire sheaf; whence it is seen that the bundle, though but a part of the sheaf, has the same number of rays as the number of rays in the w...hole. And so the sheaf and the bundle serve to exemplify again the concept of infinite manifolds.
THE OLD THEOLOGY 53 Let me now take a very simple example from the inexhaustible resources of another field. Consider the little equation, y = 2Xy which every one understands. If we assign a value, say 1, to ^, then, as we see, the value of y is thereby also determined: it is just twice as much — in this case 2; if we let ^ be %, 2/ must be 1 ; if a; be V2, y is 2 V2 ; and so on: to any value of the variable x, there corresponds one and but one value of the variable y; and conversely, for we could just as well give values to y and so find for each of them its half, or the corresponding value of ^.
What to read after The New Infinite And the Old Theology?
You can find similar books in the "Read Also" column, or choose other free books by Cassius Jackson Keyser to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Let us call the bunch of these rays a bundle. It is evident that the number of rays of the bundle is the same as the number of points in the region A, one ray through each point of A, one point of A on each ray of the bundle: this number, we have seen, is the same as the number of points on the sphere ; and this, again, the same as the number of rays of the entire sheaf; whence it is seen that the bundle, though but a part of the sheaf, has the same number of rays as the number of rays in the w...hole. And so the sheaf and the bundle serve to exemplify again the concept of infinite manifolds.
THE OLD THEOLOGY 53 Let me now take a very simple example from the inexhaustible resources of another field. Consider the little equation, y = 2Xy which every one understands. If we assign a value, say 1, to ^, then, as we see, the value of y is thereby also determined: it is just twice as much — in this case 2; if we let ^ be %, 2/ must be 1 ; if a; be V2, y is 2 V2 ; and so on: to any value of the variable x, there corresponds one and but one value of the variable y; and conversely, for we could just as well give values to y and so find for each of them its half, or the corresponding value of ^.
What to read after The New Infinite And the Old Theology?
You can find similar books in the "Read Also" column, or choose other free books by Cassius Jackson Keyser to read onlineMoreLess
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