Ads
related to: lower and upper bound maths problemseducation.com has been visited by 100K+ users in the past month
Education.com is great and resourceful - MrsChettyLife
- Printable Workbooks
Download & print 300+ workbooks
written & reviewed by teachers.
- Worksheet Generator
Use our worksheet generator to make
your own personalized puzzles.
- Educational Songs
Explore catchy, kid-friendly tunes
to get your kids excited to learn.
- Interactive Stories
Enchant young learners with
animated, educational stories.
- Printable Workbooks
Search results
Results from the WOW.Com Content Network
The set S = {42} has 42 as both an upper bound and a lower bound; all other numbers are either an upper bound or a lower bound for that S. Every subset of the natural numbers has a lower bound since the natural numbers have a least element (0 or 1, depending on convention). An infinite subset of the natural numbers cannot be bounded from above.
There is a corresponding greatest-lower-bound property; an ordered set possesses the greatest-lower-bound property if and only if it also possesses the least-upper-bound property; the least-upper-bound of the set of lower bounds of a set is the greatest-lower-bound, and the greatest-lower-bound of the set of upper bounds of a set is the least ...
The main objective of interval arithmetic is to provide a simple way of calculating upper and lower bounds of a function's range in one or more variables. These endpoints are not necessarily the true supremum or infimum of a range since the precise calculation of those values can be difficult or impossible; the bounds only need to contain the function's range as a subset.
Lebesgue's universal covering problem is an unsolved problem in geometry that asks for the convex shape of smallest area that can cover every planar set of diameter one. The diameter of a set by definition is the least upper bound of the distances between all pairs of points in the set. A shape covers a set if it contains a congruent subset.
Thus, the infimum or meet of a collection of subsets is the greatest lower bound while the supremum or join is the least upper bound. In this context, the inner limit, lim inf X n, is the largest meeting of tails of the sequence, and the outer limit, lim sup X n, is the smallest joining of tails of the sequence. The following makes this precise.
(The first exponential lower bound was obtained by Paul Erdős using the probabilistic method.) However, there is a vast gap between the tightest lower bounds and the tightest upper bounds. There are also very few numbers r and s for which we know the exact value of R(r, s). Computing a lower bound L for R(r, s) usually requires exhibiting a ...
Ads
related to: lower and upper bound maths problemseducation.com has been visited by 100K+ users in the past month
Education.com is great and resourceful - MrsChettyLife