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:
“The youngest of four sons, but not the youngest of the family!—you conceive the sort of negligence that creeps over even the kindest maternities, in such case ...”
—Walter Pater (1839–1894)
“You can’t be a Real Country unless you have A BEER and an airline—it helps if you have some kind of a football team, or some nuclear weapons, but at the very least you need a BEER.”
—Frank Zappa (1940–1993)
“He bundles every forkful in its place,
And tags and numbers it for future reference,
So he can find and easily dislodge it
In the unloading. Silas does that well.
He takes it out in bunches like birds’ nests.”
—Robert Frost (1874–1963)