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

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SUMMARY

The discussion centers on the mathematical proofs for floor and ceiling properties relevant to computer science, specifically the identity ceil(lg(n+1)) = floor(lg(n) + 1). Participants reference resources such as the Wikipedia pages on floor functions and summation properties. The inquiry seeks to identify mathematics or computer science textbooks that provide formal proofs for these properties. The consensus indicates that while the properties are useful, comprehensive proofs are often not included in standard texts.

PREREQUISITES
  • Understanding of logarithmic functions, specifically lg(n).
  • Familiarity with mathematical proofs and identities.
  • Basic knowledge of floor and ceiling functions.
  • Awareness of summation properties in mathematics.
NEXT STEPS
  • Research mathematical proofs for floor and ceiling functions in advanced mathematics textbooks.
  • Explore the "Identities" section on the Wikipedia page for summation properties.
  • Study the implications of logarithmic identities in computer science algorithms.
  • Investigate resources that cover mathematical foundations for computer science, focusing on proofs.
USEFUL FOR

Mathematicians, computer scientists, and students seeking a deeper understanding of mathematical properties that influence algorithm design and analysis.

jack1234
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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?
 
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