The Case of Sequences of Real Numbers
In mathematical analysis, limit superior and limit inferior are important tools for studying sequences of real numbers. Since the supremum and infimum of an unbounded set of real numbers may not exist (the reals are not a complete lattice), it is convenient to consider sequences in the affinely extended real number system: we add the positive and negative infinities to the real line to give the complete totally ordered set, which is a complete lattice.
Read more about this topic: Limit Superior And Limit Inferior
Famous quotes containing the words case, real and/or numbers:
“If you think dope is for kicks and for thrills, you’re out of your mind. There are more kicks to be had in a good case of paralytic polio or by living in an iron lung. If you think you need stuff to play music or sing, you’re crazy. It can fix you so you can’t play nothing or sing nothing.”
—Billie Holiday (1915–1959)
“The real genres: good and bad.”
—Franz Grillparzer (1791–1872)
“What culture lacks is the taste for anonymous, innumerable germination. Culture is smitten with counting and measuring; it feels out of place and uncomfortable with the innumerable; its efforts tend, on the contrary, to limit the numbers in all domains; it tries to count on its fingers.”
—Jean Dubuffet (1901–1985)