đẳng cấu

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The Vietnamese word "đẳng cấu" is a term used primarily in mathematics, specifically in the field of algebra and geometry. It translates to "isomorphous" in English, referring to a concept where two structures are considered the same in terms of their shape or form, even if they are represented in different ways.

Explanation:

In mathematics, when we say two objects are "đẳng cấu," it means that there is a one-to-one correspondence between the elements of the two objects that preserves the structure. This concept is often used when discussing algebraic structures, such as groups, rings, or vector spaces.

Usage Instructions:

1. Context: Use "đẳng cấu" when discussing mathematical properties, particularly in algebra or geometry.
2. Formality: This term is more formal and technical, so it is typically used in academic or professional settings.
3. Structure: It is advisable to explain the concept using examples or diagrams for better understanding.

Example:

• "Hai nhóm có cùng số phần tử và cấu trúc, vì vậy chúng là đẳng cấu." (Translation: "Two groups have the same number of elements and structure, therefore they are isomorphic.")

Advanced Usage:

• In more advanced mathematics, "đẳng cấu" can refer to more complex structures like topological spaces or category theory, where the idea of isomorphism plays a crucial role in understanding equivalences between different mathematical structures.

Word Variants:

• "đẳng cấu" itself does not have direct variants, but related terms include:
  • "đẳng cấu nhóm" (isomorphic groups)
  • "đẳng cấu không gian" (isomorphic spaces)

Different Meanings:

While "đẳng cấu" primarily refers to the mathematical concept of isomorphism, in a broader sense, it can also be applied metaphorically to describe situations where two different entities or ideas are equivalent or can be transformed into one another without losing their fundamental properties.

Academic

1. (toán học) Isomorphous