epsilon

/ep'sailən/

Thân thiện

Epsilon is the fifth letter in the Greek alphabet.

Definition

1. Noun:
   • The fifth letter of the Greek alphabet (Ε, ε): "epsilon" is the name for the fifth character in the Greek alphabet, written in uppercase as Ε and in lowercase as ε.

Usage Examples

• Noun:
  • In mathematics, epsilon (ε) often represents a very small positive quantity.
  • The Greek letter epsilon is used as a symbol in various scientific fields.

Advanced Usage

• "Epsilon-delta" (ε-δ): In calculus, this notation is used in the formal definition of a limit.

  • Understanding the epsilon-delta definition is crucial for a rigorous foundation in analysis.

• Machine Epsilon: In numerical computing, this term refers to the upper bound on the relative error due to rounding in floating-point arithmetic.

  • The value of machine epsilon depends on the specific floating-point system being used.

Variants and Related Words

• Epsilonism (n): A term occasionally used in philosophical or linguistic contexts, though rare.
• Epsilonic (adj): Pertaining to or resembling the letter epsilon (technical/rare usage).

Synonyms

• Fifth Greek letter: A descriptive synonym.
• Ε, ε: The symbolic representations.

Related Phrases

• Epsilon neighborhood: In topology and analysis, the set of points within a distance ε of a given point.

  • The concept of an epsilon neighborhood is fundamental in defining open sets.

• Epsilon closure: In automata theory, the set of states reachable from a given state on epsilon transitions (empty string transitions).

Related Idioms

Học thuật

Noun

1. the 5th letter of the Greek alphabet