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Show that there is no sequence {g_n} of continuous functions from R to R such that the sequence {(g_n)(x)} is bounded iff x is rational (where R = set of real numbers).

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- Thread starter poet_3000
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Show that there is no sequence {g_n} of continuous functions from R to R such that the sequence {(g_n)(x)} is bounded iff x is rational (where R = set of real numbers).

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lavinia

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Show that there is no sequence {g_n} of continuous functions from R to R such that the sequence {(g_n)(x)} is bounded iff x is rational (where R = set of real numbers).

Every real is the limit of a sequence of rational. The value of a continuous function on this sequence of rationals converges to its value on the limit.

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http://en.wikipedia.org/wiki/Gδ_set

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Tinyboss,

You are a clever, clever man. How did you think of something like that?

You are a clever, clever man. How did you think of something like that?

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