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"Generally speaking" suggests that the statement isn't always true. |
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Every locally constant function from the [[real number]]s '''R''' to '''R''' is constant. But the function ''f'' from the [[rational number|rationals]] '''Q''' to '''R''', defined by ''f''(''x'') = 0 for ''x'' < [[Pi|π]], and ''f''(''x'') = 1 for ''x'' > π, is locally constant (here we use the fact that π is [[irrational number|irrational]] and that therefore the two sets {''x''∈'''Q''' : ''x'' < π} and {''x''∈'''Q''' : ''x'' > π} are both [[open set|open]] in '''Q''').
Further examples include the following:
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