homogeneous

/,hɔmə'dʤi:njəs/

Thân thiện

The students in the class form a homogeneous group.

Definition

1. Adjective:
   • Consisting of parts or elements that are all of the same kind; uniform in composition or character: A homogeneous group or substance has members or components that are very similar to each other.
   • Of the same kind or nature; essentially alike: Describes things that are not mixed with different types.

Usage

The word "homogeneous" is used to describe a group, mixture, or population where the individual parts are very similar or identical in nature. It is the opposite of "heterogeneous." It is often used in scientific, mathematical, and sociological contexts.

Examples

• Adjective:
  • The mixture was stirred until it became completely homogeneous. (The mixture became uniform throughout.)
  • The school's student body is not homogeneous; it includes children from many different cultural backgrounds. (The students are not all the same.)
  • A homogeneous society shares common values and traditions. (The society is uniform in its characteristics.)

Advanced Usage

• In Mathematics: A homogeneous equation is one where all terms are of the same degree.
  • The polynomial x² + 2xy + y² is homogeneous because each term is of degree 2.
• In Chemistry/Physics: A homogeneous mixture or phase has uniform composition and properties throughout.
  • Air is considered a homogeneous mixture of gases.
• "Homogeneous of degree n": A mathematical function where scaling the inputs by a factor scales the output by a power of that factor.
  • The function f(x,y)=x²y is homogeneous of degree 3.

Variants and Related Words

• Homogeneity (noun): The quality or state of being homogeneous.
  • The homogeneity of the sample made the results reliable.
• Homogenize (verb): To make homogeneous; to blend into a uniform mixture.
  • The machine is used to homogenize milk so the cream does not separate.
• Homogenization (noun): The process of making something homogeneous.

Synonyms

• Uniform: Not varying; the same in all parts and at all times.
• Consistent: Acting or done in the same way over time.
• Alike: Similar to each other.
• Unvaried: Not exhibiting variation.

Antonyms

• Heterogeneous: Diverse in character or content; consisting of dissimilar elements.
• Mixed: Consisting of different qualities or elements.
• Varied: Incorporating a number of different types or elements.

Related Phrases/Idioms

• "Homogeneous grouping": In education, the practice of placing students with similar abilities or achievements together in a class.
  • The debate continues over the benefits of homogeneous versus heterogeneous grouping in schools.

Học thuật

Adjective

1. all of the same or similar kind or nature
   • a close-knit homogeneous group

Từ đồng nghĩa

• homogenous