There is no such thing as an interger.The ceiling function is a function which maps any variable x to the next integer, or the smallest integer greater than or equal to x. Why? Because that is how the function is defined. And there are many occasions when it is applied in normal life. If you require 3.2 cans of paint to paint a wall you will need to buy 4 cans, if a school wants to take 63 children and staff no a trip and a bus has only 30 seats, you will need three buses.
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I assume you mean the GREATEST integer function. The domain is all real numbers; the range is the integers, because the function is defined to only return integers.
The range, usually of a function, is the set of value that the function can take. The integral range is a subset of the range consisting of integer values that the function can take.
Yes.
The greatest integer function, often denoted as ⌊x⌋, gives the largest integer less than or equal to x. For 0.7, the greatest integer is 0, since 0 is the largest integer that is less than or equal to 0.7. Thus, ⌊0.7⌋ = 0.
The signed integer range extends only from negative infinity to positive infinity. You have to make up your own names and symbols for whole numbers that are not included in that range.
Signed integer is any integer that carries negative sign while unsigned integer is any integer that carries positive sign