If [a] represents the greatest internet less than or equal to a, what is the value [pi] + [-pi]?
π is 3.14159...
[π] = 3
[-π] = -4
The answer is -1 according to the answer sheet but why? I need to show the work.
To determine the value of [pi] + [-pi], we need to understand what the symbol [a] represents when applied to a number. Assuming that [a] represents the greatest integer less than or equal to a (also known as the floor function), we can proceed with finding the value.
In this case, [pi] represents the greatest integer less than or equal to pi. Since pi is approximately 3.14159, the greatest integer less than or equal to pi is 3. Therefore, [pi] = 3.
Similarly, [-pi] represents the greatest integer less than or equal to -pi. Since -pi is approximately -3.14159, the greatest integer less than or equal to -pi is -4. Therefore, [-pi] = -4.
Now we can calculate the value of [pi] + [-pi]:
[pi] + [-pi] = 3 + (-4) = -1.
So, the value of [pi] + [-pi] is -1.