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 · 2026-04-29 12:55:21

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 29 Apr 2026 - 12:55

score 378 · Answer 2 · 2026-04-29 12:54:52

378

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Epsilon-delta proof of a multivariate limit

Published on 29 Apr 2026 - 12:54

score 109 · Answer 3 · 2026-04-29 12:54:52

109

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Is this the right way to prove basic limit identities?

Published on 29 Apr 2026 - 12:54

score 352 · Answer 4 · 2026-03-24 22:10:50

352

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Multivariable Epsilon Delta Limit Proof

Published on 24 Mar 2026 - 22:10

score 83 · Answer 5 · 2026-04-16 08:23:57

83

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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 16 Apr 2026 - 8:23

score 71 · Answer 6 · 2026-04-29 12:54:55

71

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Proving this limit as $x \rightarrow ∞$?

Published on 29 Apr 2026 - 12:54

score 476 · Answer 7 · 2026-04-13 15:09:46

476

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Formally Evaluating a Limit

Published on 13 Apr 2026 - 15:09

score 58 · Answer 8 · 2026-04-29 12:55:01

58

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Complex Integral Function

Published on 29 Apr 2026 - 12:55

score 52 · Answer 9 · 2026-04-14 15:43:34

52

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

Published on 14 Apr 2026 - 15:43

score 60 · Answer 10 · 2026-04-29 12:54:57

60

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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 29 Apr 2026 - 12:54

score 287 · Answer 11 · 2026-04-29 12:54:58

287

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Proving EVT with epsilon-delta

Published on 29 Apr 2026 - 12:54

score 124 · Answer 12 · 2026-04-16 11:45:52

124

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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 16 Apr 2026 - 11:45

score 4k · Answer 13 · 2026-05-10 14:05:44

4k

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

Published on 10 May 2026 - 14:05

score 736 · Answer 14 · 2026-04-16 00:00:10

736

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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 16 Apr 2026 - 0:00

score 70 · Answer 15 · 2026-04-16 10:53:46

70

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

Published on 16 Apr 2026 - 10:53

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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