希腊字母epsilon的两种写法ϵ，ε，一般认为哪个是原型，哪个是变体？ - 知乎 注意到\epsilon的Unicode全名是「Greek Small Letter Epsilon」，即「小写希腊字母Epsilon」；而\varepsilon的Unicode全名则是「Greek Lunate Epsilon Symbol」，即「半月形希腊标志Epsilon」，并没有提到「字母」。
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 $\endgroup$
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 $\endgroup$
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
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
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)
How do you determine what $\\epsilon$ to use? - Mathematics Stack Exchange The point is that given any $\epsilon > 0$ you have make $\lvert f(x) - f(x_0)\rvert$ smaller than this randomly given $\epsilon$, by choosing (demonstrating the existence of) a $\delta > 0$ so that when $\lvert x - x_0\rvert$ is smaller than $\delta$, then $\lvert f(x) - f(x_0)\rvert$ is smaller than $\epsilon$ Let me do a simple example