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About LinkBacksGive a proof that showswhere
=0,1,2,3... is irrational.
The idea here is to show that the decimal expansion of x does not terminate or eventually repeat.
Assume that this number, call itOriginally Posted by bigb
Give a proof that shows
The idea here is to show that the decimal expansion of x does not terminate or eventually repeat., is rational, then
. And thus by this it means we can write
where
is eventually repeating. Therefore,
. But the only way to express zero in a decimal expansion is trivially i.e.
. But then this implies that
must also be eventually repeating which is a contradiction because it is an increasing sequence. Contradiction.
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