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Function discontinuous at all integers and continuous everywhere

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My teacher gave the class a few examples of functions that are continuous at all integers and discontinuous everywhere else. He then asked us if it is possible to have a function that is discontinuous at all integers and continuous everywhere else. He informed us that there is and that we should try finding it and a graph to show it's a function for mathematics practice.

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A function that is discontinuous at all integers and continuous everywhere else is found. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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The step function f(x)=[x] is discontinuous at every integer and continuous at other points.
f(x)=[x] is defined ...

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