Examples of Limits of Nets
- Limit of a sequence and limit of a function: see below.
- Limits of nets of Riemann sums, in the definition of the Riemann integral. In this example, the directed set is the set of partitions of the interval of integration, partially ordered by inclusion.
Read more about this topic: Net (mathematics)
Famous quotes containing the words examples of, examples, limits and/or nets:
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (16701733)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (15331592)
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we dont happen to have all the data. In mathematics we have all the data ... and yet we dont understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (19091943)
“The philosopher caught in the nets of language.”
—Friedrich Nietzsche (18441900)