Below you will find example sentences with "upper bound". The examples show how this phrase is used in natural context and which words often surround it.

Upper Bound in a sentence

Corpus data

  • Displayed example sentences: 20
  • Discovered as a combination around: upper
  • Corpus frequency in the collocation scan: 16
  • Phrase length: 2 words
  • Average sentence length: 31.1 words

Words in this phrase

upper bound

Meanings of words in this phrase

  • upper can mean: At a higher level, rank or position. Frequent word
  • bound can mean: simple past and past participle of bind Frequent word

Sentence profile

  • Phrase position: 4 start, 11 middle, 5 end
  • Sentence types: 20 statements, 0 questions, 0 exclamations

Usage patterns

These patterns show short text windows around the phrase in the example sentences:

a least upper bound 3× 5 50 upper bound in this 1× a least upper bound then is 1× also an upper bound it is 1× an asymptotic upper bound and θ 1× and constant upper bound on its 1× below the upper bound though except 1× called an upper bound of s 1×

Sentence openings and endings

Common sentence openings:

minimal upper bounds 2× a description of 1× a set a 1× a set s 1× although is also 1× bekenstein used this 1×

Common sentence endings:

least upper bound 4× a fixed number 1× a lowpass filter 1× a red diamond 1× an upper bound 1× are similarly defined 1×

Context words

These words often appear near this phrase in the example sentences:

set 10× real 6× bounds 5× numbers 4× lower 4× ordered 3× property 3× nonempty 3× supremum 3× minimal 3× directed 3× rate 3×

Related phrases

upper deck lower bound upper secondary upper east upper atmosphere upper body upper egypt upper left upper stage upper portion

Phrases around this combination

Other phrases discovered around upper:

upper east 10× upper body 9× upper left 8× upper stage 8×

Just before it in the phrase index:

upper body upper atmosphere upon thousands upon millions upon hundreds upon dozens

Just after it in the phrase index:

upper deck upper east upper egypt upper left upper portion upper secondary

Other phrases with the same pattern

Same start:

upper deck upper secondary upper east upper atmosphere upper body upper egypt

Same ending:

lower bound

Corpus analysis

  • The phrase "upper bound" has 2 words and usually appears in the middle in these examples. The average sentence has 31.1 words and is mostly made up of statements.
  • Around this phrase, patterns and context words such as a least upper bound, 5 50 upper bound in this, set, real and bounds stand out.
  • In the phrase index, this combination connects with upper deck, lower bound, upper secondary, upper east, upper body and upper left, linking the page to nearby combinations.

Example types with upper bound

This selection groups the examples by length and sentence type, making usage of the full phrase easier to scan:

Short example sentences

Although is also an upper bound, it is not the "least upper bound" and hence is not the "supremum". (19 words)

Minimal upper bounds Finally, a partially ordered set may have many minimal upper bounds without having a least upper bound. (20 words)

Minimal upper bounds are those upper bounds for which there is no strictly smaller element that also is an upper bound. (21 words)

Longer example sentences

A set S of real numbers is called bounded from above if there is a real number k such that k ≥ s for all s in S. The number k is called an upper bound of S. The terms bounded from below and lower bound are similarly defined. (48 words)

Central banks come back into the spotlight in the week ahead, and while the Fed is all but certain to maintain the Fed Funds rate at its current 5.50% upper bound in this meeting, the focus will be on the outlook for future rate hikes. (46 words)

Together these give an upper bound for the unique fraction that generates a cycle of length n. If this upper bound is smaller than the largest number for which the conjecture has been verified to hold, then a cycle of length n is impossible. (44 words)

Example sentences (20)

If an ordered set has the property that every nonempty subset of having an upper bound also has a least upper bound, then is said to have the least-upper-bound property.

Moreover, the set of Dedekind cuts has the least-upper-bound property, i.e., every nonempty subset of it that has any upper bound has a least upper bound.

Although is also an upper bound, it is not the "least upper bound" and hence is not the "supremum".

The real numbers are uniquely picked out (up to isomorphism ) by the properties of a Dedekind complete ordered field, meaning that any nonempty set of real numbers with an upper bound has a least upper bound.

Thus, because of the O(n log n) upper bound on heapsort's running time and constant upper bound on its auxiliary storage, embedded systems with real-time constraints or systems concerned with security often use heapsort.

Together these give an upper bound for the unique fraction that generates a cycle of length n. If this upper bound is smaller than the largest number for which the conjecture has been verified to hold, then a cycle of length n is impossible.

Minimal upper bounds are those upper bounds for which there is no strictly smaller element that also is an upper bound.

Minimal upper bounds Finally, a partially ordered set may have many minimal upper bounds without having a least upper bound.

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Tajikistan is right on the edge, gaining just 0.84 percent in the paper’s “upper bound” scenario and dropping by 0.04 in the “lower bound” projection.

A set S of real numbers is called bounded from above if there is a real number k such that k ≥ s for all s in S. The number k is called an upper bound of S. The terms bounded from below and lower bound are similarly defined.

Bekenstein used this to put an upper bound on the entropy in a region of space, and the bound was proportional to the area of the region.

Summary of running times In the following time complexities citation O(f) is an asymptotic upper bound and Θ(f) is an asymptotically tight bound (see Big O notation ).

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.

While the definition of a directed set is for an "upward-directed" set (every pair of elements has an upper bound), it is also possible to define a downward-directed set in which every pair of elements has a common lower bound.

A set A of real numbers (blue balls), a set of upper bounds of A (red diamond and balls), and the smallest such upper bound, that is, the supremum of A (red diamond).

Various uses Baseband bandwidth A baseband bandwidth is equal to the highest frequency of a signal or system, or an upper bound on such frequencies, citation for example the upper cut-off frequency of a Lowpass filter.

Central banks come back into the spotlight in the week ahead, and while the Fed is all but certain to maintain the Fed Funds rate at its current 5.50% upper bound in this meeting, the focus will be on the outlook for future rate hikes.

The number of excess natural deaths are still below the upper bound though, except for the Free State, Mpumalanga and the North West.

But the university can feasibly prepare for worst-case scenarios: the upper bound on voter turnout is, after all, a fixed number.

A description of a function in terms of big O notation usually only provides an upper bound on the growth rate of the function.

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