Floor Function

The function is the largest Integer , shown as the dashed curve in the above plot, and also calledthe Greatest Integer Function. In many computer languages, the floor function is called the Integer Partfunction and is denoted int(x). The name and symbol for the floor function were coined by K. E. Iverson (Graham et al. 1990).

Unfortunately, in many older and current works (e.g., Shanks 1993, Ribenboim 1996), the symbol is used instead of. Because of the elegant symmetry of the floor function and Ceiling Function symbols and, and because is such a useful symbol when interpreted as an Iverson Bracket, the use of todenote the floor function should be deprecated. In this work, the symbol is used to denote the nearest integerNint function since it naturally falls between the and symbols.

References

Graham, R. L.; Knuth, D. E.; and Patashnik, O. ``Integer Functions.'' Ch. 3 in Concrete Mathematics: A Foundation for Computer Science. Reading, MA: Addison-Wesley, pp. 67-101, 1990.

Iverson, K. E. A Programming Language. New York: Wiley, p. 12, 1962.

Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, pp. 180-182, 1996.

Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, p. 14, 1993.

Spanier, J. and Oldham, K. B. ``The Integer-Value Int() and Fractional-Value frac() Functions.'' Ch. 9 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 71-78, 1987.

• Counting Number
• Coupon Collector's Problem
• Covariance
• Covariance Matrix
• Covariant Derivative
• Covariant Tensor
• Covariant Vector
• Cover
• Covering
• Covering Dimension
• Covering System
• Cover Relation
• Coversine
• Coxeter Diagram
• Coxeter-Dynkin Diagram
• Coxeter Graph
• Coxeter Group
• Coxeter Matrix
• Coxeter's Loxodromic Sequence of Tangent Circles
• Coxeter-Todd Lattice
• Cox's Theorem
• Cramer's Rule
• Cramér Conjecture
• Cramér-Euler Paradox
• Cramér's Theorem