In calculus, an infinitesimal quantity. Geeks have been known to use it in non-math-related conversations, as in "Celine Dion doesn't *completely* suck, but she's epsilon away from it."

epoch = E = epsilon squared

epsilon

[see delta] 1. n. A small quantity of anything. "The cost is epsilon." 2. adj. Very small, negligible; less than marginal. "We can get this feature for epsilon cost." 3. `within epsilon of': close enough to be indistinguishable for all practical purposes, even closer than being `within delta of'. "That's not what I asked for, but it's within epsilon of what I wanted." Alternatively, it may mean not close enough, but very little is required to get it there: "My program is within epsilon of working."

--The Jargon File version 4.3.1, ed. ESR, autonoded by rescdsk.

{computer science} Epsilon is used to repesent the smallest value that a floating point number (a real number on the computer) can hold such that it satisfies the equation


    R (1.0 + epsilon) not equal to R (1.0)

    where the function R maps a real number to a
    representation that uses a finite amount of
    computer memory (limited precision).

It is often used as a stopping criteria for algorithms since a change less than epsilon would not result in the change in a floating point value as represented in the computer's memory.

Epsilon for an 8 byte IEEE floating point number is about 2.2 x 10-16 and is defined as DBL_EPSILON in the C standard library in the header file "float.h".

In computer science, when dealing with finite automata and regular expressions, epsilon (ε) is used to denote "the empty string". It should be noted that ε, ∅, and {ε} are all different things (this is a common mistake made by beginning CS students). ε is of type "string", whereas ∅ and {ε} are of type "set of strings"; ∅ does not contain ε, whereas {ε} (obviously) does. However, ∅* is equivalent to ε. ε is the identity for concatenation:

εR ≡ Rε ≡ R

Regular expressions in UNIX have extended operations beyond the basic three (union, concatenation, and closure); however, they can all be represented by standard regular expressions. The '?' operation in UNIX regular expressions stands for 'zero or one occurrences of'; i.e., R? is the same as (R | ε).

In a finite automaton, a transition on ε means the automaton moves from one state to another without consuming a character; automatons with epsilon-transitions are one type of non-deterministic finite automaton. Epsilon-transitions are necessary to convert regular expressions into finite automata.

Fifth letter of the Greek alphabet, capital Ε and lower-case ε. The lower-case letter has two equally correct variant forms, one like a reversed 3 and the other a 'c' with a middle stroke, like ∈. The HTML codes for it are Ε and ε

In English the name is often pronounced with the stress on the first syllable, as in Epsom, and this is also the accentuation of the Modern Greek. An older English pronunciation stresses the long I, ep-SI-lon as in Simon, in accord with the Latin quantity.

It derives from the Phoenician letter for H, related to Hebrew ה he and Arabic ه ha. The Semitic scripts used only consonant symbols, but the Greeks used some of those they didn't need as vowels, creating the first true alphabet.

The letter was adopted into the Roman alphabet via Etruscan as E, and into the Cyrillic alphabet as the same shape Е.

In Ancient Greek it had the pronunciation of E in bet, when short, and in Modern Greek it has kept this sound. The ancient diphthong αι AI also has this E sound in Modern Greek. There is no distinction of vowel length in Modern, but in Ancient Greek Ε was originally used as a long vowel also; in fact two distinct long vowels. In around 400 BCE a spelling reform was introduced in Athens. They shifted to a system already used by the Ionian Greeks, using the combination ΕΙ for a long mid-close vowel (as in German Seele) and Η eta for a long mid-open vowel (German Bär), leaving plain epsilon for the short vowel.

The original name of the letter was just ei (that is, just e before the reform). Then it became e psilon 'bare E' to distinguish it from the letter eta, which until then they had used as an aspirate: see also psilosis.

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