Epsilon: meaning, definitions and examples
๐
epsilon
[ หษpsษชlษn ]
mathematics term
Epsilon is a small positive quantity in mathematics used to denote an arbitrarily small positive number, typically in the context of limits and continuity in calculus. It is often used in epsilon-delta definitions of limits to establish how close a function approaches a certain value. In other contexts, epsilon can denote an error margin or tolerance in numerical analysis, making it crucial for defining precision. Additionally, the Greek letter 'ฮต' symbolizes this term in mathematical expressions.
Synonyms
error margin, small quantity, tolerance.
Examples of usage
- In calculus, we say a function approaches a limit as the delta goes to zero and the epsilon can be any small positive number.
- To ensure accuracy in our calculations, we adjust the epsilon value to suit the required precision.
- The epsilon notation provides a rigorous definition of convergence in sequences.
Translations
Translations of the word "epsilon" in other languages:
๐ต๐น รฉpsilon
๐ฎ๐ณ เคเคชเฅเคธเคฟเคฒเฅเคจ
๐ฉ๐ช Epsilon
๐ฎ๐ฉ epsilon
๐บ๐ฆ ะตะฟััะปะพะฝ
๐ต๐ฑ epsilon
๐ฏ๐ต ใคใใทใญใณ
๐ซ๐ท epsilon
๐ช๐ธ รฉpsilon
๐น๐ท epsilon
๐ฐ๐ท ์ ์ค๋ก
๐ธ๐ฆ ุฅุจุณูููู
๐จ๐ฟ epsilon
๐ธ๐ฐ epsilon
๐จ๐ณ ฮตpsilon
๐ธ๐ฎ epsilon
๐ฎ๐ธ epsilon
๐ฐ๐ฟ ัะฟัะธะปะพะฝ
๐ฌ๐ช แแแกแแแแแ
๐ฆ๐ฟ epsilon
๐ฒ๐ฝ รฉpsilon
Etymology
The term 'epsilon' originates from the Greek alphabet, where it denotes the fifth letter (ฮ, ฮต). The use of epsilon in mathematical contexts can be traced back to the developments in calculus by mathematicians such as Augustin-Louis Cauchy and Karl Weierstrass in the 19th century. They utilized this symbol to express the concept of limits and continuity, laying down a rigorous framework for analysis. The epsilon-delta definition of limits introduced a more formal approach to understanding the behavior of functions as they approach values, which became foundational in mathematical analysis. Over time, epsilon has become integral in various fields of mathematics, physics, and engineering, symbolizing both small quantities and acceptable error margins in computations. Its widespread use signifies its importance in establishing precision in both theoretical and applied mathematics.