What is the value of [tex]$\lfloor-12\rfloor$[/tex]?
Answer (1)
The problem asks for the value of the floor function of -12.
The floor function, denoted by ⌊ x ⌋ , returns the greatest integer less than or equal to x .
Since -12 is an integer, ⌊ − 12 ⌋ = − 12 .
Therefore, the value of ⌊ − 12 ⌋ is − 12 .
Explanation
Understanding the Floor Function We are asked to find the value of ⌊ − 12 ⌋ , which represents the floor function applied to the number -12. The floor function, denoted as ⌊ x ⌋ , returns the greatest integer less than or equal to x . In simpler terms, it rounds the number down to the nearest integer.
Applying the Definition Since -12 is already an integer, the floor function of -12 is simply -12. There's no need to round down because -12 is an integer itself.
Final Answer Therefore, ⌊ − 12 ⌋ = − 12 .
Examples
The floor function is used in computer science to determine the index of an array or a list. For example, if you have an array and you want to access an element using a non-integer index, you would use the floor function to round the index down to the nearest integer. This ensures that you are accessing a valid element in the array. Another example is in everyday life, such as when calculating how many whole items you can buy with a certain amount of money when the items have a non-integer price. You can only buy a whole number of items, so you use the floor function to find the maximum number of items you can afford.
