Greatest integer function
Basically ⌊x⌋ = the greatest INTEGER smaller or equal to xFor example:⌊4.8⌋ = 4 ⌊6.5⌋ = 6. ⌊π⌋= 3Also, the greatest integer function is also called the floor function and on a graph it looks like a staircase
The greatest integer function, also known as the floor function, is a mathematical function that rounds down a given real number to the closest integer less than or equal to the given number. It is denoted by the symbol ⌊ x ⌋, where x is the real number.
For example, ⌊ 2.5 ⌋ = 2 and ⌊ -3.7 ⌋ = -4.
The greatest integer function can also be defined using the following notation:
⌊ x ⌋ = n, where n is an integer and n ≤ x < n + 1. Some important properties of the greatest integer function are: 1. it is a step function, which means that it jumps from one integer to the next as its argument crosses an integer value. 2. it is a periodic function, meaning that it repeats itself after each integer value. 3. it has discontinuities at each integer value, where the value of the function changes abruptly. 4. it is also a useful tool in solving inequalities and working with periodic functions. Overall, the greatest integer function is an important mathematical function that has many applications in various fields, including mathematics, engineering, and computer science.
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