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:
“Not infrequently, we encounter copies of important human beings; and here, too, as in the case of paintings, most people prefer the copies to the originals.”
—Friedrich Nietzsche (18441900)
“Main Street was never the same. I read Gide and tried to
translate Proust. Now nothing is real except French wine.
For absurdity is reality, my loneliness unreal, my mind tired.
And I shall die an old Parisian.”
—Conrad Kent Rivers (19331968)
“The forward Youth that would appear
Must now forsake his Muses dear,
Nor in the Shadows sing
His Numbers languishing.”
—Andrew Marvell (16211678)