bao hàm

Học thuật

Thân thiện

Bao hàm là một khái niệm quan trọng trong toán học.

Definition

Verb:
- To imply, to contain, to encompass: "bao hàm" indicates that something contains or includes a certain meaning, characteristic, or element within its scope or nature. It often refers to an abstract or inherent inclusion.
- To involve, to entail: It can also mean that one thing logically or necessarily leads to or includes another as a part of its consequence or definition.

Usage Examples

Verb:
- Khái niệm này bao hàm nhiều ý nghĩa sâu sắc. (This concept implies many profound meanings.)
- Quyền lợi đi đôi với nghĩa vụ, quyền tự do cũng bao hàm trách nhiệm. (Rights come with obligations; the right to freedom also entails responsibility.)
- Một định nghĩa chính xác phải bao hàm tất cả các đặc điểm cơ bản. (An accurate definition must encompass all the essential features.)

Advanced Usage

Logical or Necessary Inclusion: Used to express that one element is inherently or logically contained within another.
- Việc chấp nhận điều khoản này bao hàm sự đồng ý của bạn với tất cả các điều kiện. (Accepting this clause implies your agreement to all the conditions.)
In Mathematics (Logic/Set Theory): The term can be used in the context of "inclusion" (sự bao hàm).
- Mối quan hệ bao hàm giữa hai tập hợp. (The inclusion relationship between two sets.)

Variants and Related Words

Sự bao hàm (Noun): The act of implying or the state of being implied/included.
- Sự bao hàm ý nghĩa trong thơ ca thường rất tinh tế. (The implication of meaning in poetry is often very subtle.)
Bao gồm (Verb): To include, to comprise. (Note: "Bao gồm" is often used for more concrete or listed inclusions, while "bao hàm" is more abstract.)
- Phí dịch vụ bao gồm thuế VAT. (The service fee includes VAT.)

Synonyms

Ẩn chứa: To contain, to hold within (often something hidden or intrinsic).
Hàm chứa: To contain, to bear within (similar to "bao hàm," often used interchangeably).
Kéo theo: To entail, to lead to (focusing on logical consequence).

Related Phrases (Collocations)

Bao hàm ý nghĩa: To imply meaning.
- Câu nói đó bao hàm ý nghĩa châm biếm. (That statement implies a sarcastic meaning.)
Bao hàm mâu thuẫn: To contain/involve a contradiction.
- Lập luận của anh ấy tự nó bao hàm mâu thuẫn. (His argument itself contains a contradiction.)

Related Idioms

(Note: "Bao hàm" itself is not typically used in fixed idiomatic expressions. Its usage is more academic or logical.)

Bao hàm là một khái niệm quan trọng trong toán học.

verb