Explore BrainMass

Explore BrainMass

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

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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
    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.

    $2.49

    ADVERTISEMENT