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Date: 10-7-2020
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Date: 17-8-2020
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Date: 12-8-2020
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If is any number and
and
are integers, then there is a rational number
for which
![]() |
(1) |
If is irrational and
is any whole number, there is a fraction
with
and for which
![]() |
(2) |
Furthermore, there are an infinite number of fractions for which
![]() |
(3) |
(Hilbert and Cohn-Vossen 1999, pp. 40-44).
Hurwitz has shown that for an irrational number
![]() |
(4) |
there are infinitely rational numbers if
, but if
, there are some
for which this approximation holds for only finitely many
.
REFERENCES:
Hilbert, D. and Cohn-Vossen, S. Geometry and the Imagination. New York: Chelsea, p. 41, 1999.
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