xry or yrx if every pair of distinct elements in partial order are comparablethen the order is called total order or linear order example for the integersthe relations and <both define partial orders operation is total order becausefor every pair of integers and such that yeither or likewise<is total order becausefor every pair of integers and such that yeither < or < example for the powerset of the integersthe subset operator defines partial order (because it is antisymmetric and transitivefor example{ { howeversets { and { are not comparable by the subset operatorbecause neither is subset of the other thereforethe subset operator does not define total order on the powerset of the integers miscellaneous notation units of measurei use the following notation for units of measure "bwill be used as an abbreviation for bytes"bfor bits"kbfor kilobytes ( bytes)"mbfor megabytes ( bytes)"gbfor gigabytes ( bytes)and "msfor milliseconds ( millisecond is of secondspaces are not placed between the number and the unit abbreviation when power of two is intended thus disk drive of size gigabytes (where gigabyte is intended as byteswill be written as " gb spaces are used when decimal value is intended an amount of bits would therefore be written " kbwhile " kbrepresents bits milliseconds is written as ms note that in this book large amounts of storage are nearly always measured in powers of two and times in powers of ten factorial functionthe factorial functionwritten nfor an integer greater than is the product of the integers between and ninclusive thus as special case the factorial function grows quickly as becomes larger because computing the factorial function directly is time-consuming processit can be useful to have an equation that provides good approximation stirling' approximation states that pnne ) where ( is the base for the system of natural logarithms thus we see that the symbol "means "approximately equal