Net (mathematics) - Limit Superior

Limit Superior

Limit superior and limit inferior of a net of real numbers can be defined in a similar manner as for sequences. Some authors work even with more general structures than the real line, like complete lattices.

For a net we put

Limit superior of a net of real numbers has many properties analogous to the case of sequences, e.g.

where equality holds whenever one of the nets is convergent.

Read more about this topic:  Net (mathematics)

Famous quotes containing the words limit and/or superior:

    Can you find out the deep things of God? Can you find out the limit of the Almighty?
    Bible: Hebrew, Job 11:7.

    The First Amendment is not a blanket freedom-of-information act. The constitutional newsgathering freedom means the media can go where the public can, but enjoys no superior right of access.
    George F. Will (b. 1934)