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I know it has to involve radical 2 but because that is the only number we know is irrational but other than that I have no idea.

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In summary, the conversation discusses constructing a nest of closed, bounded intervals in the field of formal rational functions to show that the Nested Intervals property fails in this field. This involves using an irrational number, such as sqrt2, as the center of the intervals and considering what happens as the intervals get smaller. The conversation also touches on the topology of the field and the subtlety of irrational numbers not being included in the intervals.

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I know it has to involve radical 2 but because that is the only number we know is irrational but other than that I have no idea.

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Kb13 said:In the field offormal rational functions, construct a nest of closed, bounded intervals whose intersection is empty. (That is, show that the Nested Intervals property fails in this field)

Is there a topology assumed for this field? If so, what is it? I'm not sure what an "interval" looks like in this field.

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