the greatest integer function
The greatest integer function, denoted as [x] or sometimes as floor(x), is a mathematical function that rounds down a real number to the largest previous integer
The greatest integer function, denoted as [x] or sometimes as floor(x), is a mathematical function that rounds down a real number to the largest previous integer. It essentially gives you the greatest integer that is less than or equal to the given number.
To illustrate with examples:
1. [5] = 5: Since 5 is already an integer, the greatest integer function simply returns the input as is, so [5] is equal to 5.
2. [-2.5] = -3: In this case, the greatest integer less than or equal to -2.5 is -3, so the greatest integer function returns -3.
3. [1.9] = 1: Here, the greatest integer less than or equal to 1.9 is 1, so [1.9] is equal to 1.
4. [0] = 0: Since 0 is an integer, the greatest integer function returns 0.
5. [-7] = -7: As -7 is already an integer, the greatest integer function simply returns the input as is, so [-7] is equal to -7.
In summary, the greatest integer function rounds down real numbers to the nearest lesser or equal integer. This function is used in various mathematical applications, such as defining step functions or solving problems involving floor values.
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