What does the greatest integer function return?

The greatest integer function, often denoted as ⌊x⌋, returns the largest integer that is less than or equal to a given number x. This means that it rounds down to the nearest whole number.

For example, if you have a number like 3.7, the greatest integer function would return 3, since 3 is the largest integer that is less than or equal to 3.7. Similarly, for a number like -2.3, it would return -3, because -3 is the greatest integer that is less than -2.3.

This function is especially useful in various mathematical applications, including computer science where it might be used to determine indices or in algorithms that require whole numbers. Understanding how this function behaves with both positive and negative numbers is key to applying this knowledge correctly in mathematical problems.