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epsilon    音标拼音: ['ɛpsəl,ɑn]
n. 希腊语字母之第五字

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  • analysis - What does $\epsilon$ mean in this formula - Mathematics . . .
    $\begingroup$ As an aside, the $\in$ takes its basic shape from the Greek letter $\epsilon$ The symbol $\in$ means "is an element of", so using the Greek letter that starts the word "element" as a design inspiration isn't entirely unreasonable $\endgroup$
  • notation - What does the letter epsilon signify in mathematics . . .
    $\begingroup$ Historically, the symbol $\in$ is derived from $\epsilon$, thus it is not impossible to confuse both symbols Also, not as ubiquitous as its primary usage, this Greek symbol $\epsilon$ or $\varepsilon$ is also used to denote the sign, including Levi-Civita symbol in physics and random sign in probability to name a few $\endgroup$
  • Understanding epsilon delta continuity definition - Mathematics Stack . . .
    $$\le |(x - x_{0})|^{2} + |2x_{0}(x-x_{0})| < \epsilon$$ by the triangle inequality But we don't know this is less than epsilon since we now have something that is greater than what we actually know is less than epsilon, this comes up time and time again in many proofs and I can't get my head around why we say this is still less than epsilon
  • notation - Backwards epsilon - Mathematics Stack Exchange
    The backwards epsilon notation for "such that" was introduced by Peano in 1898, e g from Jeff Miller's Earliest Uses of Various Mathematical Symbols: Such that According to Julio González Cabillón, Peano introduced the backwards lower-case epsilon for "such that" in "Formulaire de Mathematiques vol II, #2" (p iv, 1898)
  • What is the epsilon-delta definition of limits, exactly?
    The epsilon-delta definition of limit says that if you want f(x) to be arbitrary close to a value L as x approaches a, i e $\displaystyle lim_{x \to a} f(x)= L$, all you need to do as that you find a delta such that the distance between x and a is smaller than delta
  • calculus - Original source of precise ε-δ (epsilon-delta) formal . . .
    I frequently see Karl Weierstrass credited for formulating the precise definition of a limit But what I'd like to know is the origin of the formal definition so common in textbooks, that given a
  • notation - Why exactly was $\epsilon$ chosen to denote a very small . . .
    $\begingroup$ See the post: Who gave you the epsilon ?: Cauchy in his 1823 textbook used trhe Greek letters $\alpha, \beta, \gamma, \delta, \epsilon, \ldots$ for "nombres très-petites" (very small numbers) In the first chapter he started using $\alpha$ and $\beta$ and in the proof of the Theorem (7th Lecture) he introduced $\delta$ and
  • elementary set theory - Epsilon numbers - Mathematics Stack Exchange
    Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
  • real analysis - Does the epsilon-delta definition of limits truly . . .
    We experience motion as a continuous event, and so when we want to talk about continuity, we talk in terms of change and motion Epsilon delta uses the absolute value of a difference to express spatial dimension, and it appeals to the Continuum, the reals, for the notion of continuity
  • Good Explanation of Epsilon-Delta Definition of a Limit?
    In the game our opponents value of epsilon and our responding value of delta must always be strictly greater than zero Saying "$\epsilon = 0$" or "$\delta = 0$" isn't an allowed move in the game; Our opponents aren't going to win by throwing larger values of $\epsilon$ at us because we can just repeat our previous $\delta$ and win that round





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