How do you use Boolean in a sentence? See 10+ example sentences showing how this word appears in different contexts, including synonyms like mathematician, plus the exact meaning.
Boolean meaning
- Of or pertaining to the work of George Boole.
- Pertaining to data items that can have “true” and “false” (or, equivalently, 1 and 0 respectively) as their only possible values and to operations on such values.
Synonyms of Boolean
Using Boolean
- The main meaning on this page is: Of or pertaining to the work of George Boole. | Pertaining to data items that can have “true” and “false” (or, equivalently, 1 and 0 respectively) as their only possible values and to operations on such values.
- Useful related words include: mathematician.
- In the example corpus, boolean often appears in combinations such as: boolean algebra, of boolean, the boolean.
Context around Boolean
- Average sentence length in these examples: 23.1 words
- Position in the sentence: 11 start, 9 middle, 0 end
- Sentence types: 20 statements, 0 questions, 0 exclamations
Corpus analysis for Boolean
- In this selection, "boolean" usually appears near the start of the sentence. The average example has 23.1 words, and this corpus slice is mostly made up of statements.
- Around the word, infinite, generalized, positive, algebra, ring and algebras stand out and add context to how "boolean" is used.
- Recognizable usage signals include a boolean algebra with, a boolean or flag and boolean ring. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "boolean" sits close to words such as acuity, ademola and albans, which helps place it inside the broader word index.
Example types with boolean
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
Thus every Boolean ring becomes a Boolean algebra. (8 words)
Generalized Boolean lattices are exactly the ideals of Boolean lattices. (10 words)
The categories of Boolean rings and Boolean algebras are equivalent. (10 words)
Furthermore, a subset of a Boolean ring is a ring ideal (prime ring ideal, maximal ring ideal) if and only if it is an order ideal (prime order ideal, maximal order ideal) of the Boolean algebra. (36 words)
In Boolean-valued semantics (for classical propositional logic ), the truth values are the elements of an arbitrary Boolean algebra, "true" corresponds to the maximal element of the algebra, and "false" corresponds to the minimal element. (35 words)
Historically, the term "Boolean ring" has been used to mean a "Boolean ring possibly without an identity", and "Boolean algebra" has been used to mean a Boolean ring with an identity. (31 words)
Example sentences (20)
Historically, the term "Boolean ring" has been used to mean a "Boolean ring possibly without an identity", and "Boolean algebra" has been used to mean a Boolean ring with an identity.
A Boolean algebra with only one element is called a trivial Boolean algebra or a degenerate Boolean algebra.
For infinite Boolean algebras this is no longer true, but every infinite Boolean algebra can be represented as a subalgebra of a power set Boolean algebra (see Stone's representation theorem ).
Treatment of non-boolean values in boolean expressions In most dialects of Lisp including Common Lisp, by convention the value NIL evaluates to the value false in a boolean expression.
A map between two Boolean rings is a ring homomorphism if and only if it is a homomorphism of the corresponding Boolean algebras.
Furthermore, a subset of a Boolean ring is a ring ideal (prime ring ideal, maximal ring ideal) if and only if it is an order ideal (prime order ideal, maximal order ideal) of the Boolean algebra.
Generalizations Removing the requirement of existence of a unit from the axioms of Boolean algebra yields "generalized Boolean algebras".
Generalized Boolean lattices are exactly the ideals of Boolean lattices.
Handling this ambiguity was an early problem of the theory, reflecting the modern use of both Boolean rings and Boolean algebras (which are simply different aspects of one type of structure).
In Boolean-valued semantics (for classical propositional logic ), the truth values are the elements of an arbitrary Boolean algebra, "true" corresponds to the maximal element of the algebra, and "false" corresponds to the minimal element.
In fact, one can show that any finite Boolean algebra is isomorphic to the Boolean algebra of the power set of a finite set.
In this context the decision is a boolean expression composed of conditions and zero or more boolean operators.
It had no data memory or data registers; instructions could test Boolean input signals, set or clear Boolean output signals, jump conditional or unconditionally, or call a subroutine.
Note that the tautology problem for positive Boolean formulae remains co-NP complete, even though the satisfiability problem is trivial, as every positive Boolean formula is satisfiable.
The categories of Boolean rings and Boolean algebras are equivalent.
The quotient ring R/I of any Boolean ring R modulo any ideal I is again a Boolean ring.
Thus every Boolean ring becomes a Boolean algebra.
Digital Science CEO said: “Boolean queries were a foundational approach for navigating the limitations of 1990s search technologies.
A Boolean or Flag type is a type which can represent only two values: 0 and 1, usually identified with false and true respectively.
Add six fresh boolean variables a, b, c, d, e, and f, to be used to simulate this clause and no other.
Phrases with boolean
These phrases have their own page with example sentences containing the full combination:
Common combinations with boolean
These word pairs occur most frequently in English texts:
- boolean algebra 26×
- of boolean 14×
- the boolean 14×
- boolean ring 11×
- boolean algebras 11×
- and boolean 5×
- in boolean 5×
- boolean rings 4×
- is boolean 4×
- boolean operators 4×