All-operator is a term that is often used in computer science and mathematics. It is an operator that is used to represent the universal quantifier, which means “for all.” The all-operator is used to describe a condition that applies to all members of a set.
Definitions
The all-operator is a symbol that is used in mathematical logic to indicate that a statement is true for every element in a set. It is represented by the symbol “∀” and is read as “for all” or “for every.” The all-operator is used to describe a condition that applies to every member of a set.
Origin
The all-operator has its origins in mathematical logic and was first introduced by the mathematician Gottlob Frege in the late 19th century. It is now widely used in computer science and other fields that rely on mathematical logic.
Meaning in different dictionaries
The all-operator is not commonly found in dictionaries, but it is defined in some mathematical and computer science dictionaries. In these dictionaries, it is defined as an operator that represents the universal quantifier, which means “for all.”
Associations
The all-operator is closely associated with mathematical logic and is used in many different branches of mathematics, including set theory, number theory, and algebra. It is also used in computer science to describe algorithms and programming languages.
Synonyms
The all-operator is sometimes referred to as the universal quantifier, which means “for all.” It is also sometimes referred to as the “for every” operator.
Antonyms
The opposite of the all-operator is the existential quantifier, which means “there exists.” This operator is represented by the symbol “∃” and is used to describe a condition that applies to at least one member of a set.
The same root words
The all-operator is derived from the Latin word “omnis,” which means “all” or “every.” This word is also the root of many other English words, including “omniscient,” which means “all-knowing,” and “omnipotent,” which means “all-powerful.”
Example Sentences
Here are some example sentences that use the all-operator:
- ∀x ∈ S, x > 0 (For all x in the set S, x is greater than 0.).
- ∀n ∈ N, n is even or n is odd (For all natural numbers n, n is either even or odd.).
- ∀x ∈ R, ∃y ∈ R, x + y = 0 (For all real numbers x, there exists a real number y such that x + y = 0.).