Infinity: An Essay in MetaphysicsClarendon Press, 1964 - 289 pagina's |
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Pagina 22
... sum of the infinite series 1-1 + 1- 1 + 1-1 & c . If we take the successive partial sums of the series , we generate the sequence I - I = 0 , 0 + 1 = I , I - I = 0 , 0 + 1 = 1 , & c . This sequence of partial sums clearly fails to ...
... sum of the infinite series 1-1 + 1- 1 + 1-1 & c . If we take the successive partial sums of the series , we generate the sequence I - I = 0 , 0 + 1 = I , I - I = 0 , 0 + 1 = 1 , & c . This sequence of partial sums clearly fails to ...
Pagina 25
... series : if o , then the series would seem to contain an even number of terms ; if 1 , an odd number ; both of which ... infinite convergent series 1 / 2 + 1 / 4 + 1 / 8 , & c . can add up to 1 only on the condition that the infinite ...
... series : if o , then the series would seem to contain an even number of terms ; if 1 , an odd number ; both of which ... infinite convergent series 1 / 2 + 1 / 4 + 1 / 8 , & c . can add up to 1 only on the condition that the infinite ...
Pagina 122
... infinite series . The word ' end ' occurs twice in the argument , and unfortun- ately it is employed in two different senses . It is important to distinguish three types of infinite series . First , there is the series represented by ...
... infinite series . The word ' end ' occurs twice in the argument , and unfortun- ately it is employed in two different senses . It is important to distinguish three types of infinite series . First , there is the series represented by ...
Inhoudsopgave
INFINITY | 1 |
HYPERMATHEMATICS | 72 |
COSMOLOGY I | 102 |
Copyright | |
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absolutely actual infinite actual infinitesimal aleph-null argument Aristotle Brouwer Cantor certainly code number concept of number convergent series cosmological count countable decimal expansion denumerable discourse divergent series earth empirical entails equal exist fact falsifiable finite proof finitist follows formula geometry Grandi's series Hence Hyperboreans hypothesis inch infinite distance infinite number infinite sequence infinite series infinitesimal infinitum infinity insist integers intelligible interval Kant Leibniz logical Löwenheim-Skolem theorem mathe mathematician mathematics matics mean merely metaphysical minim minute natural numbers non-denumerable number of stars object ontological open end order-type paradox Peano postulates philosophy physics pluriverse possible potential infinite precisely predicates prime twin principle priori proof number proto-concept prove punct question random numbers rational real numbers rule seen sense serrated continuum Space spatial speaking standard concept straight line sum-total suppose Swahilis theorem thesis things transfinite tropological uncountable vulgar concept whole Wittgenstein word Z-series Zeno procedure