Solution 1.1:7d

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Visserligen finns ett repetitivt mönster i decimalutvecklingen
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There is, admittedly, a repeating pattern in the decimal expansion
::<math>0,\underline{10}\ \underline{100}\ \underline{1000}\ \underline{10000}\ \underline{100000}\,\ldots</math>
::<math>0,\underline{10}\ \underline{100}\ \underline{1000}\ \underline{10000}\ \underline{100000}\,\ldots</math>
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men för att det ska vara ett rationellt tal måste decimalutvecklingen efter en viss decimal bestå av en fix sifferkombination som oavbrutet upprepar sig. Någon sådan upprepning finns inte i decimalutvecklingen ovan (siffergruppen 10, 100, 1000, 10000, ... växer hela tiden i storlek). Talet är alltså inte rationellt.
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but for it to be a rational number, the decimal expansion must, after a certain decimal place, consist of a combination of digits that repeat themselves indefinitely. There is no such repetition in the
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decimal expansion given above (the digit groups
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10, 100, 1000, 10000, ...increase in size all the time). The
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number is therefore not rational.
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Revision as of 14:02, 14 September 2008

There is, admittedly, a repeating pattern in the decimal expansion

\displaystyle 0,\underline{10}\ \underline{100}\ \underline{1000}\ \underline{10000}\ \underline{100000}\,\ldots

but for it to be a rational number, the decimal expansion must, after a certain decimal place, consist of a combination of digits that repeat themselves indefinitely. There is no such repetition in the decimal expansion given above (the digit groups 10, 100, 1000, 10000, ...increase in size all the time). The number is therefore not rational.

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