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# Functions that are continuous at all integers and discontinuous everywhere else.

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My teacher gave the class a few examples of functions that are discontinuous at all integers and continuous everywhere else. He then asked us if it is possible to have a function that is continuous at all integers and discontinuous 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.

https://brainmass.com/math/graphs-and-functions/functions-that-are-continuous-at-all-integers-and-discontinuous-everywhere-else-76815

#### Solution Preview

First let me give you one function which is discontinuous at all integers but continuous at all other points.

We define f(x)=n whenever n<=x<n+1 where n is an integer and x is any real number.
Let me explain the nature this function.
Suppose x=2.03, which means 2<x<3, hence f(x)=2.
Similarly for any value between 2 and 3(inclusive of 2) f(x) will be ...

#### Solution Summary

Functions that are continuous at all integers and discontinuous everywhere else are investigated. The solution is detailed and well presented.

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