If is any number and is any Integer, 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) |
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 .
© 1996-9 Eric W. Weisstein
1999-05-25