Greatest Integer Function

This cheat sheet covers two important functions – the Greatest Integer Function and the Fractional Part Function.

greatest integer function

These two functions are quite important and find their way in many problems related to calculus. The two functions are related to each other and many problems related are solved easily when one function is expressed in the form of the other.

One must have a strong understanding of the graphs of both these functions, as this will help in easily solving many problems that are otherwise difficult to solve without using graphical methods. Many tricky problems in limits and continuity involve the use of both these functions. A cheat sheet on Limits is also available on this website.

Also, these two functions occur quite frequently in problems related to definite integration and area under curves. Cheat sheets on Definite Integrals and Area Under Curves are also available on this website.

This one page PDF covers summarised theory and the most important formulas related to the concept. Keep it handy while you’re revising the concept, especially before an exam.

The topics included in this cheat sheet are:

  • Definition of the Greatest Integer Function
  • Properties of the Greatest Integer Function
  • Inequalities related to the Greatest Integer Function
  • Definition of the Fractional Part Function
  • Properties of the Fractional Part Function
  • Inequalities related to the Fractional Part Function

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