finitely

Thân thiện

There are finitely many apples in the basket.

Definition

Adverb 1. In a finite manner; within a finite or limited scope or quantity: The word "finitely" describes an action or state that is bounded, has an end, or is not infinite. It is the adverbial form of "finite."

Usage

"Finitely" is used to modify verbs, adjectives, or other adverbs to indicate that something is limited, countable, or has a definite boundary. It is often used in mathematical, logical, scientific, and general academic contexts.

Examples

• The resources are finitely available, so we must use them wisely.
• A Turing machine can only have a finitely long tape at any given time.
• Although the set of prime numbers is infinite, any specific list of them is finitely long.
• The universe may or may not be finitely old; scientists continue to debate this.

Advanced Usage

• "finitely many": A common phrase in mathematics and logic meaning a limited, countable number, as opposed to "infinitely many."
  • For a given perimeter, there are only finitely many possible shapes with integer side lengths.
• "finitely generated": A technical term in algebra (e.g., group theory, ring theory) describing a structure that can be produced from a finite set of elements.
  • A finitely generated abelian group has a finite basis.
• "finitely additive": A term in measure theory describing a property of certain set functions.
  • The function is finitely additive but not countably additive.

Variants and Related Words

• Finite (adjective): Having limits or bounds; not infinite.
  • The company has a finite budget for the project.
• Finiteness (noun): The quality or state of being finite.
  • The finiteness of human life is a central theme in philosophy.
• Infinite (adjective): Opposite of finite; limitless or endless in space, extent, or size.
• Infinitely (adverb): Opposite of finitely; to an infinite extent or degree.

Synonyms

• Limitedly
• Boundedly
• Terminably
• Countably (in specific mathematical contexts)

Antonyms

• Infinitely
• Endlessly
• Boundlessly
• Limitlessly

Học thuật

Adverb

1. with a finite limit
   • there are finitely many solutions to this problem