The quantifier of existence is the meaning of existence.

Definition of universal quantifier: the phrases "all", "every", "any one", "any one" and "everything" contained in mathematical sentences are within the prescribed scope, indicating the whole or all meanings. Such words are called universal quantifiers. A proposition that contains a full-name quantifier is called a universal proposition. The negation of universal quantifier is existential quantifier.

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In some full-name propositions, sometimes full-name quantifiers can be omitted. For example, a prism is a polyhedron, which means "all prisms are polyhedrons".

The words 1, "to all people" and "to any one person" are logically called universal quantifiers and recorded as "?" A proposition that contains a full-name quantifier is called a universal proposition.

For any x in m, p(x) holds, and it is recorded as "?" x∈M，p(x).

Read: Every X belongs to M, which makes p(x) hold.

2. Words such as "you yi" and "at least one" are logically called existential quantifiers and recorded as "?" Propositions containing existential quantifiers are called special propositions.

There is at least one x in M, which makes p(x) hold, and it is recorded as "?" x∈M，p(x).

Read: read: there is an x belonging to m, which makes p(x) hold.

Negative:

1. For the full name proposition P: "?" The negation of x∈M and p(x) ┐p is: "?" x∈M,┐p(x)。

2. For the special proposition containing quantifiers P: "?" The negation of x∈M and p(x) ┐p is: "?" x∈M,┐p(x)。

General statement

Full-name proposition: The formula is "All S are P". Full-name proposition can be expressed by full-name quantifiers, adverbs such as "Du" and subjects such as "Everyone", sometimes without any quantifier symbol, such as "Human beings are wise." Because algebraic theorems use full-name quantifiers, each algebraic theorem is a particularly strong condition. It is also the full-name quantifier that makes the identity transformation by bringing in rules become the core of algebraic reasoning.

Existential quantifier

Definition: The phrases "some", "at least one", "one" and "existence" all mean individuals or parts. Such words are called existential quantifiers. Propositions containing existential quantifiers are called special propositions. Special proposition: The special proposition whose formula is "Some S is p" uses existential quantifiers, such as "some" and "few", and can also use "basically", "general" and "just some". Propositions containing existential quantifiers are also called existential propositions. The phrases "you yi" and "at least one" are usually called existential quantifiers in logic, and the symbol is "?" Express delivery. Propositions containing existential quantifiers are called special propositions (existential propositions).

Propositions containing existential quantifiers are called special propositions (existential propositions).

For example:

(1) has a prime number that is not odd;

Some parallelograms are rhombic.

Common existential quantifiers are "You", "You Yi", "You Yi" and "You".

Special proposition "There is an X in M, which makes p(x) hold". Jane wrote:? x ∈ M，p(x)

Read: there is an x that belongs to m, which makes p(x) hold.