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.© BrainMass Inc. brainmass.com November 30, 2021, 1:00 am ad1c9bdddf
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 ...
Functions that are continuous at all integers and discontinuous everywhere else are investigated. The solution is detailed and well presented.