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The wikipedia page floor and ceiling functions furthermore lists a lot of properties very few proofs or derivations though.
Sum of floor of e. Sum d j 1 k lfloor n d rfloor sum d lfloor n k rfloor 1 lfloor n j rfloor lfloor n d rfloor k lfloor n k rfloor j lfloor n j rfloor this is corollary 4 in some inversion formulas for sums of quotients. The floor is the truncated float value i e. Volume 36 number 5 2006 1595 1602. And floor n 2 2 floor n 2 1.
The e 4 series are specially modified from the boeing 747 200b for the national emergency airborne command post neacp program the e 4 serves as a survivable mobile command post for the national command. The result is their sum or total beside numbers other types of values can be summed as well. The function must return an integer representing the floor of the sum of two floating point numbers. For instance floor 1 1 3 05 floor 4 15 4.
Most of the material presented in this article can be found in some form in concrete mathematics by r. Functions vectors matrices polynomials and in general elements of any type of mathematical objects on which an operation denoted is defined. For example and while. This is an application of the following fun result i published with natalio guersenzvaig a few years ago.
The boeing e 4 advanced airborne command post aacp the current nightwatch aircraft is a strategic command and control military aircraft operated by the united states air force usaf. A summation formula for sequences involving floor and ceiling functions. In mathematics summation is the addition of a sequence of any kind of numbers called addends or summands. In mathematics and computer science the floor function is the function that takes as input a real number and gives as output the greatest integer less than or equal to denoted or similarly the ceiling function maps to the least integer greater than or equal to denoted or.
Anything after the decimal point is dropped. The other piece in the puzzle is the expression for the sum of an arithmetic sequence which can be found here.
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