Are There Proofs for Floor and Ceiling Properties in Computer Science?

[jack1234]

Some floor and ceiling properties like
ceil(lg(n+1))=floor(lg(n)+1)
and "Some properties of ceiling function" section under "http://en.wikipedia.org/wiki/Floor_function"

and summation properties like
"Identities" section under "http://en.wikipedia.org/wiki/Sum"
prove to me very useful for computer science study.

But I am interesting of their proof. Does any mathematics book or computer science book has provide proofs for the properties mentioned above?

 

[Kummer]

Your question was asked here.