48. Let f be a function defined on ]0, 1[ by : 0, if x is irrational f (x) = {1/g, if x=p/q; where p and q are positive integers having no common factor. Prove that f is continuous at each irrational...

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48. Let f be a function defined on ]0, 1[ by :<br>0, if x is irrational<br>f (x) = {1/g, if x=p/q; where p and q are positive<br>integers having no common factor.<br>Prove that f is continuous at each irrational point and discontinuous<br>at each rational point.<br>

Extracted text: 48. Let f be a function defined on ]0, 1[ by : 0, if x is irrational f (x) = {1/g, if x=p/q; where p and q are positive integers having no common factor. Prove that f is continuous at each irrational point and discontinuous at each rational point.

Jun 04, 2022

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48. Let f be a function defined on ]0, 1[ by : 0, if x is irrational f (x) = {1/g, if x=p/q; where p and q are positive integers having no common factor. Prove that f is continuous at each irrational...

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