The notation [x ] stands for the greatest integer that is less than or equal to x. Calculate [-1,2]
I assume you refer to the floor function, namely ⌊x⌋ represents the greatest integer which is less than or equal to x.
You can figure this out by drawing the given number x on the number line, and the next integer equal to or to the left of the given number is then ⌊x⌋.
For example,
⌊4.5⌋ = 4
⌊3⌋ = 3
⌊-0.4⌋ = -1
⌊-2⌋ = -2
⌊-10.2⌋ = -11
In the case given,
⌊1,2⌋ is not clear, because the floor function takes only one number as the argument, unless the "," is meant to be a decimal symbol, which is current in French speaking countries.
In that case,
⌊-1,2⌋
= ⌊-1.2⌋
= -2
To calculate the expression [-1,2], we use the notation [x] which represents the greatest integer that is less than or equal to x. Let's break down the calculation step by step.
1. [-1,2] means that we need to find the greatest integer that is less than or equal to both -1 and 2.
2. Starting with -1, the greatest integer that is less than or equal to -1 is -1 itself. Therefore, we have the value of [-1] = -1.
3. Moving on to 2, the greatest integer that is less than or equal to 2 is 2 itself. Thus, we have the value of [2] = 2.
4. Since [-1,2] requires finding the greatest integer that is less than or equal to both -1 and 2, we take the minimum value between the results of steps 2 and 3. In this case, the minimum between -1 and 2 is -1.
Therefore, the value of [-1,2] is -1.
Ah, the greatest integer function, also known as the floor function. It's like taking a giant hammer and smashing the decimal part of a number. So, when we apply it to the range from -1 to 2, we have:
[-1,2] = [-1] + [0] + [1] = -1 + 0 + 1 = 0
So, the result is 0! It's as if the floor function magically balanced everything out.
To evaluate the expression [-1,2], we need to find the greatest integer that is less than or equal to both -1 and 2.
The greatest integer less than or equal to -1 is -1.
The greatest integer less than or equal to 2 is 2.
Since -1 is less than 2, the common greatest integer that is less than or equal to both -1 and 2 is -1.
Therefore, the value of [-1,2] is -1.