1. Existence means that all elements in a set have one or more consistency, that is, at least one consistency.

2. Arbitrary means that all elements in a set are consistent, that is, no element is consistent.

Second, the parts of speech are different:

1. Existence is a mathematical noun, which mainly refers to the quantifier of existence.

2. Arbitrary is a full-name quantifier. Full-name quantifiers refer to words that contain phrases such as "full quantity", "every", "arbitrary" and "everything" within a specified range, indicating the meaning of all objects within a specified range or the whole specified range.

Three, the applicable proposition types are different:

1, any suitable full-name proposition: a proposition with a full-name quantifier is called a full-name proposition. The negation of universal quantifier is existential quantifier. Full-name propositions can be expressed by full-name quantifiers, or by the repetition of subjects such as "everyone", or even without any quantifier symbols, such as "all mankind is wise."

2. Existence is suitable for special propositions, and propositions containing existential quantifiers are called special propositions. For the full name proposition p:? The negation of x∈M and p(x) ┐p is:? x∈M,┐p(x)。 For the special proposition p:? The negation of x∈M and p(x) ┐p is:? x∈M,┐p(x)。

Baidu Encyclopedia-Existence

Baidu encyclopedia-full name quantifier