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The greatest integer function is a function that results in the integer nearer to the given real number. It is also called the step function. The greatest integer function rounds off the given number to the nearest integer. Hence, the formula to find the greatest integer is very simple.
Here, you will learn domain and range of greatest integer function and properties of greatest integer function with example. Let’s begin – Greatest Integer Function or Floor Function. For any real number x, we use the symbol [x] or \(\lfloor x \rfloor\) to denote the greatest integer less than or equal to x. For example,
5 Απρ 2024 · The greatest Integer Function [X] indicates an integral part of the real number x x which is the nearest and smaller integer to x x . It is also known as the floor of X. [x]=the largest integer that is less than or equal to x. In general: If, n n <= X X < n+1 n+1 . Then, (n \epsilon Integer)\Longrightarrow [X]=n (nϵI nteger) [X]=n.
The domain and range of the greatest integer function are R and Z respectively. It is also known as the floor of X where [x] denotes the largest integer that is less than or equal to x. Hence the greatest integer function is clearly rounding off to the greatest integer that is less than or equivalent to the provided number.
3 Αυγ 2023 · The domain of the greatest integer function is a group of real numbers divided into intervals like [-4, 3), [-3, 2), [-2, 1), and [-1, 0). The corresponding ranges are the integers obtained from the function. For example, Properties. The common properties are: ⌊x⌋ = x, where x is an integer. ⌊x + n⌋ = ⌊x⌋ + n, where n ∈ Z. ⌊-x] = –⌊x], if x ∈ Z.
Muskan Shafi. Content Writer. Greatest Integer Function is a function that gives the greatest integer which is less than or equal to a given real number. It is a function that rounds up the number to the nearest integer less than or equal to the given number. Greatest Integer Function is also referred to as ‘ Step Function ’.
