Question

Why is it $|f(x) - L| < \epsilon$ in the definition for a limit and not $0 < |f(x) - L| < \epsilon$?

score 2.2k · Answer 1 · 2018-01-27 20:48:49

2.2k

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Why is it $|f(x) - L| < \epsilon$ in the definition for a limit and not $0 < |f(x) - L| < \epsilon$?

Published on 27 Jan 2018 - 20:48

score 376 · Answer 2 · 2026-03-24 00:25:13

376

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Epsilon-delta proof of a multivariate limit

Published on 24 Mar 2026 - 0:25

score 105 · Answer 3 · 2026-03-17 11:58:24

105

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Is this the right way to prove basic limit identities?

Published on 17 Mar 2026 - 11:58

score 351 · Answer 4 · 2026-03-23 04:47:18

351

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Multivariable Epsilon Delta Limit Proof

Published on 23 Mar 2026 - 4:47

score 80 · Answer 5 · 2018-02-03 09:38:28

80

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if $f: D\subseteq \mathbb{R}^n \to R$ is continuous at $a \in D$, then there exists a $\delta > 0$ s.t $f$ is continuous on $B(a, \delta)$?

Published on 03 Feb 2018 - 9:38

score 67 · Answer 6 · 2026-03-17 07:11:54

67

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Proving this limit as $x \rightarrow ∞$?

Published on 17 Mar 2026 - 7:11

score 472 · Answer 7 · 2026-03-16 22:12:20

472

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Formally Evaluating a Limit

Published on 16 Mar 2026 - 22:12

score 53 · Answer 8 · 2026-03-16 20:15:46

53

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Complex Integral Function

Published on 16 Mar 2026 - 20:15

score 48 · Answer 9 · 2026-03-16 20:36:32

48

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When does $|f(x)-L| = 0$?

Published on 16 Mar 2026 - 20:36

score 56 · Answer 10 · 2018-02-13 18:16:59

56

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What is the meaning of "Parries" in "Choose $\delta > 0$ such that $\delta$ parries $\varepsilon$ for this uniform continuity of $f$.

Published on 13 Feb 2018 - 18:16

score 282 · Answer 11 · 2026-03-17 03:51:06

282

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Proving EVT with epsilon-delta

Published on 17 Mar 2026 - 3:51

score 121 · Answer 12 · 2018-02-17 23:46:49

121

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$f, g$ continuous on closed finite interval, $f(x) > g(x)$ for all $x$ from the interval, implies $f(x) > g(x) + \alpha$ for some $\alpha > 0$?

Published on 17 Feb 2018 - 23:46

score 4k · Answer 13 · 2018-02-19 10:18:10

4k

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Proving or disproving $e^{x^2}$ and $e^{-x^2}$ is uniformly continuous with $\epsilon - \delta$

Published on 19 Feb 2018 - 10:18

score 733 · Answer 14 · 2018-02-20 20:27:15

733

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Help with Multivariable Delta-Epsilon Proof for $\lim_{(x,y)\to (1,2)}{ \left(2x^2 + y^2\right)} = 6$

Published on 20 Feb 2018 - 20:27

score 67 · Answer 15 · 2018-02-22 07:52:35

67

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Prove that if $f(x)=L$ for deleted neighbourhood of $a$ then $\frac1{f(x)}=\frac1L$

Published on 22 Feb 2018 - 7:52

List Question

Why is it $|f(x) - L| < \epsilon$ in the definition for a limit and not $0 < |f(x) - L| < \epsilon$?

Epsilon-delta proof of a multivariate limit

Is this the right way to prove basic limit identities?

Multivariable Epsilon Delta Limit Proof

if $f: D\subseteq \mathbb{R}^n \to R$ is continuous at $a \in D$, then there exists a $\delta > 0$ s.t $f$ is continuous on $B(a, \delta)$?

Proving this limit as $x \rightarrow ∞$?

Formally Evaluating a Limit

Complex Integral Function

When does $|f(x)-L| = 0$?

What is the meaning of "Parries" in "Choose $\delta > 0$ such that $\delta$ parries $\varepsilon$ for this uniform continuity of $f$.

Proving EVT with epsilon-delta

$f, g$ continuous on closed finite interval, $f(x) > g(x)$ for all $x$ from the interval, implies $f(x) > g(x) + \alpha$ for some $\alpha > 0$?

Proving or disproving $e^{x^2}$ and $e^{-x^2}$ is uniformly continuous with $\epsilon - \delta$

Help with Multivariable Delta-Epsilon Proof for $\lim_{(x,y)\to (1,2)}{ \left(2x^2 + y^2\right)} = 6$

Prove that if $f(x)=L$ for deleted neighbourhood of $a$ then $\frac1{f(x)}=\frac1L$

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