The greatest integer function returns the largest integer smaller than the number you provide it. That is, if n ≤ x < n + 1, where n is an integer, then the "greatest integer of x" is [x] = n.

• Let n be even. Then we can write n = 2k for some integer k ≥ 0. Now,

[n/2] = [k] = k

while

[-n/2] = [-k] = -k

so that

[n/2] - [-n/2] = 2k = n

• Let n be odd. Then n = 2k + 1 for some integer k ≥ 0. Every odd integer occurs between two even integers, so that

n - 1 < n < n + 1

or equivalently,

2k < n < 2k + 2

so that

k < n/2 < k + 1

It follows that [n/2] = k.

Similarly, if we negative the previous inequality, we have

-k > -n/2 > -(k + 1), or -k - 1 < -n/2 < -k

which means [-n/2] = -k - 1.

So we make the same conclusion,

[n/2] - [-n/2] = k - (-k - 1) = 2k + 1 = n

3 0

2 years ago

8- (0.75+2). Plzzz explain it

frosja888 [35]

Answer:

5.25

Step-by-step explanation:

ok so first you add 0.75+2 which is equal to 2.75

and now you will have 8-2.75 which is equal to 5.25

3 0

3 years ago

Warren picked 3/4 of a pound of strawberries. That afternoon, Warrens

Ludmilka [50]

Answer:

she ate 6 ounces

Step-by-step explanation:one pound is 16 ounces 3\4 of a pound is 12 ounces half of 12 is 6 ounces

5 0

3 years ago