The greatest integer function ,shows below, is defined to be greatest________less than or equal to x.
f(x)=[[x]]
less
integer
Integer
The greatest integer function, denoted as [[x]], is a mathematical function that takes a real number x as input and returns the greatest integer less than or equal to x. In other words, it rounds down x to the nearest whole number.
To determine the value of [[x]], you follow these steps:
1. If x is already a whole number (integer), then [[x]] is equal to x. For example, [[3]] = 3.
2. If x is a decimal number, [[x]] is the largest integer that is less than or equal to x. For example, [[3.8]] = 3, [[-2.4]] = -3.
3. If x is a negative decimal number, [[x]] is the largest integer that is less than x. For example, [[-4.5]] = -5.
It is important to note that the greatest integer function only considers the integer part of the number and does not take into account any fractional or decimal portion.