Limit Of A Sequence
As the positive integer n becomes larger and larger, the value n sin(1/n) becomes arbitrarily close to 1. We say that "the limit of the sequence n sin(1/n) equals 1."
In mathematics, a limit of a sequence is a value that the terms of the sequence "get close to eventually". If such a limit exists, the sequence converges.
Limits can be defined in any metric or topological space, but are usually first encountered in the real numbers.
Convergence of sequences is a fundamental notion in mathematical analysis, which has been studied since ancient times.
Read more about Limit Of A Sequence: Definition in Hyperreal Numbers, History
Famous quotes containing the words limit of, limit and/or sequence:
“Berowne they call him, but a merrier man,
Within the limit of becoming mirth,
I never spent an hour’s talk withal.”
—William Shakespeare (1564–1616)
“Today, the notion of progress in a single line without goal or limit seems perhaps the most parochial notion of a very parochial century.”
—Lewis Mumford (1895–1990)
“Reminiscences, even extensive ones, do not always amount to an autobiography.... For autobiography has to do with time, with sequence and what makes up the continuous flow of life. Here, I am talking of a space, of moments and discontinuities. For even if months and years appear here, it is in the form they have in the moment of recollection. This strange form—it may be called fleeting or eternal—is in neither case the stuff that life is made of.”
—Walter Benjamin (1892–1940)