Get to know Bounded better with 10+ real example sentences, the meaning and synonyms like delimited or finite.
Bounded in a sentence
Related words
Bounded meaning
simple past and past participle of bound
Using Bounded
- The main meaning on this page is: simple past and past participle of bound
- Useful related words include: delimited, finite.
- In the example corpus, bounded often appears in combinations such as: bounded by, is bounded, of bounded.
Context around Bounded
- Average sentence length in these examples: 26.6 words
- Position in the sentence: 10 start, 7 middle, 3 end
- Sentence types: 20 statements, 0 questions, 0 exclamations
Corpus analysis for Bounded
- In this selection, "bounded" usually appears near the start of the sentence. The average example has 26.6 words, and this corpus slice is mostly made up of statements.
- Around the word, totally, terms, locally, non, poset and automaton stand out and add context to how "bounded" is used.
- Recognizable usage signals include 5 favourite bounded clear to and a totally bounded subset under. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "bounded" sits close to words such as abba, abdomen and anomaly, which helps place it inside the broader word index.
Example types with bounded
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
It is a bounded concept. (5 words)
Bounded and totally bounded spaces Diameter of a set. (9 words)
Intervals that are bounded at only one end are said to be half-bounded. (14 words)
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)
Bounded non-determinism An NTM has the property of bounded non-determinism, i.e., if an NTM always halts on a given input tape T then it halts in a bounded number of steps, and therefore can only have a bounded number of possible configurations. (45 words)
Note that this concept of boundedness has nothing to do with finite size, and that a subset S of a bounded poset P with as order the restriction of the order on P is not necessarily a bounded poset. (39 words)
Example sentences (20)
Bounded non-determinism An NTM has the property of bounded non-determinism, i.e., if an NTM always halts on a given input tape T then it halts in a bounded number of steps, and therefore can only have a bounded number of possible configurations.
If a sequence is both bounded from above and bounded from below, then the sequence is said to be bounded.
An infinite subset of the rational numbers may or may not be bounded from below and may or may not be bounded from above.
An interval is said to be left-bounded or right-bounded if there is some real number that is, respectively, smaller than or larger than all its elements.
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.
Bounded and totally bounded spaces Diameter of a set.
However, the discrete metric space is free in the category of bounded metric spaces and Lipschitz continuous maps, and it is free in the category of metric spaces bounded by 1 and short maps.
In engineering applications, a function corresponding to a linear time-invariant (LTI) system is stable if every bounded input produces a bounded output.
In particular, any continuously differentiable function is locally Lipschitz, as continuous functions are locally bounded so its gradient is locally bounded as well.
Intervals that are bounded at only one end are said to be half-bounded.
Moreover, a function ƒ defined on a bounded interval is Riemann-integrable if and only if it is bounded and the set of points where f is discontinuous has Lebesgue measure zero.
Note that this concept of boundedness has nothing to do with finite size, and that a subset S of a bounded poset P with as order the restriction of the order on P is not necessarily a bounded poset.
Properties and uses seeAlso Equivalence to linear bounded automaton A formal language can be described by a context-sensitive grammar if and only if it is accepted by some linear bounded automaton (LBA).
The converse does not hold, since any infinite set can be given the discrete metric (one of the examples above) under which it is bounded and yet not totally bounded.
The image of a totally bounded subset under a uniformly continuous function is totally bounded.
The terms bounded above (bounded below) are also used in the mathematical literature for sets that have upper (respectively lower) bounds.
Variants Bounded Pareto distribution seeAlso infobox The bounded (or truncated) Pareto distribution has three parameters α, L and H. As in the standard Pareto distribution α determines the shape.
As the buzzer sounded, Caruso bounded off the court, clenching his fists as he tipped his head back and let out a scream.
It is a bounded concept.
Once in the clear, the 2/5 favourite bounded clear to win by a length and a half from the Aidan O’Brien-trained Meditate with Jim Bolger’s Comhra a head away in third place.
Common combinations with bounded
These word pairs occur most frequently in English texts:
- bounded by 68×
- is bounded 46×
- of bounded 14×
- be bounded 11×
- bounded from 8×
- bounded and 8×
- bounded to 8×
- and bounded 7×
- area bounded 7×
- totally bounded 5×