In this exercise, we are asked to calculate the values of the functions floor and ceiling.
Definitions:
“The floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x)” Source.
a)⌈3/4⌉
⌈3/4⌉=⌈0.75⌉=1
b)⌊7/8⌋
⌊7/8⌋=⌊0.875⌋=0
c) ⌈−3/4⌉
⌈−3/4⌉=⌈−0.75⌉=0
d)⌊−7/8⌋
⌊−7/8⌋=)⌊−0.875⌋ = -1
e) ⌈3⌉
⌈3⌉=3
f) ⌊−1⌋
⌊−1⌋ = -1
g)⌊1/2+⌈3/2⌉⌋
⌊1/2+⌈3/2⌉⌋=⌊0.5+⌈1.5⌉⌋=⌊0.5+2⌋=⌊2.5⌋=2
h)⌊1/2·⌊5/2⌋⌋
⌊1/2·⌊5/2⌋⌋=⌊0.5·⌊2.5⌋⌋=⌊0.5·2⌋=⌊1⌋=1
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