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Wondering how to use Supremum in a sentence? Below are 10+ example sentences from authentic English texts. Including the meaning .

Rare word

Supremum in a sentence

Supremum meaning

(real analysis): Given a subset X of R, the smallest real number that is ≥ every element of X; (order theory): given a subset X of a partially ordered set P (with partial order ≤), the least element y of P such that every element of X is ≤ y.

Using Supremum

  • The main meaning on this page is: (real analysis): Given a subset X of R, the smallest real number that is ≥ every element of X; (order theory): given a subset X of a partially ordered set P (with partial order ≤), the least element y of P such that every element of X is ≤ y.
  • In the example corpus, supremum often appears in combinations such as: the supremum, supremum of, both supremum.

Context around Supremum

  • Average sentence length in these examples: 23.3 words
  • Position in the sentence: 2 start, 11 middle, 7 end
  • Sentence types: 20 statements, 0 questions, 0 exclamations

Often before:

limit 2×

Often after:

limit 1× limsup 1× operators 1× join 1×

Sentence patterns with Supremum

These short patterns come directly from the example sentences and show how the word is often embedded:

is the supremum of the 3× both a supremum and an 2× and its supremum 1× and the supremum by the 1× both a supremum join and 1× consequently the supremum is also 1× has a supremum 1× if the supremum of a 1×

Sentence openings and endings

Common sentence openings:

the infimum is 2× a set a 1× although is also 1× as a linear 1× by analogy with 1× consequently the supremum 1×

Common sentence endings:

a red diamond 1× a specker sequence 1× all bounded sequences 1× an infimum meet 1× and an infimum 1× and its supremum 1×

Words around Supremum

Just before it in the word index:

supremos 4 supremo 91 supremes 23 supremely 121 supreme 7.187 suprematist 2

Just after it in the word index:

supress 2 supressed 3 supri 2 suprise 10 suprised 5 suprising 4

Similar in corpus frequency:

abra 34 accies 34 accommodative 34 acerbic 34 achebe 34 actualise 34

Corpus analysis for Supremum

  • In this selection, "supremum" usually appears in the middle of the sentence. The average example has 23.3 words, and this corpus slice is mostly made up of statements.
  • Around the word, limit, limit, limsup and operators stand out and add context to how "supremum" is used.
  • Recognizable usage signals include is the supremum of the and both a supremum and an. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "supremum" sits close to words such as abra, accies and accommodative, which helps place it inside the broader word index.

Example types with supremum

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

Hence, it is the supremum of the limit points. (9 words)

Definition A real set with upper bounds and its supremum. (10 words)

If the supremum of a subset S exists, it is unique. (11 words)

Longer example sentences

For instance, a lattice is a partially ordered set in which all finite subsets have both a supremum and an infimum, and a complete lattice is a partially ordered set in which all subsets have both a supremum and an infimum. (41 words)

For example, if one uses the classical definition of a sequence, the set of computable numbers is not closed under the basic operation of taking the supremum of a bounded sequence (for example, consider a Specker sequence ). (37 words)

By analogy with the above, in the domain of the extended reals, negative infinity is the identity element for the maximum and supremum operators, while positive infinity is the identity element for minimum and infimum. (35 words)

Example sentences (20)

For instance, a lattice is a partially ordered set in which all finite subsets have both a supremum and an infimum, and a complete lattice is a partially ordered set in which all subsets have both a supremum and an infimum.

Limit inferior is also called infimum limit, liminf, inferior limit, lower limit, or inner limit; limit superior is also known as supremum limit, limit supremum, limsup, superior limit, upper limit, or outer limit.

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

As a linear continuum The order on the number line Each set on the real number line has a supremum.

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).

By analogy with the above, in the domain of the extended reals, negative infinity is the identity element for the maximum and supremum operators, while positive infinity is the identity element for minimum and infimum.

Consequently, the supremum is also referred to as the least upper bound (or LUB).

Definition A real set with upper bounds and its supremum.

Advertentie

For example, if one uses the classical definition of a sequence, the set of computable numbers is not closed under the basic operation of taking the supremum of a bounded sequence (for example, consider a Specker sequence ).

Hence, it is the supremum of the limit points.

Here sup is the supremum with respect to the orderings in X and Y, respectively.

If the supremum of a subset S exists, it is unique.

In mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet).

In medical parlance concerning a lesion or in geology concerning a rock, the diameter of an object is the supremum of the set of all distances between pairs of points in the object.

One also defines the ∞ -norm using the supremum : : and the corresponding space ℓ ∞ of all bounded sequences.

That is, : Similarly, the limit superior of a set X is the supremum of all of the limit points of the set.

The greatest lower bound on this sequence of joins of tails is :: :So the limit supremum is contained in all subsets which are upper bounds for all except finitely many sets of the sequence.

The infimum is given by the intersection of topologies, and the supremum by the topology generated by the union of topologies.

The infimum is in a precise sense dual to the concept of a supremum.

The Kolmogorov–Smirnov statistic for a given cumulative distribution function F(x) is : where sup x is the supremum of the set of distances.

Advertentie

Common combinations with supremum

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "supremum" in a sentence?
An example: "For instance, a lattice is a partially ordered set in which all finite subsets have both a supremum and an infimum, and a complete lattice is a partially ordered set in which all subsets have both a supremum and an infimum." This page contains 10+ example sentences with the word "supremum" from authentic English texts.
What does "supremum" mean?
Supremum means: (real analysis): Given a subset X of R, the smallest real number that is ≥ every element of X; (order theory): given a subset X of a partially ordered set P (with partial order ≤), the least element y of P such that every element of X is ≤ y.
How many example sentences with "supremum" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "supremum", drawn from a database of millions of English sentences.