Question

Can we rephrase Epsilon-delta definition?

score 209 · Answer 1 · 2023-02-15 05:01:38

209

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Can we rephrase Epsilon-delta definition?

Published on 15 Feb 2023 - 5:01

score 71 · Answer 2 · 2023-02-18 16:56:13

71

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Proving a limit exists by using epsilon delta definition

Published on 18 Feb 2023 - 16:56

score 125 · Answer 3 · 2026-03-29 20:38:49

125

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$\forall x$ versus $\exists x$ in the definition of limit

Published on 29 Mar 2026 - 20:38

score 372 · Answer 4 · 2023-02-28 22:29:42

372

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Let f:(X, $d_X$) → (Y, $d_Y$). Show f continuous if and only if ∀x ∈ X and ∀ε > 0, exists δ > 0 such that ∀y ∈ X, dX(x , y) < δ ⇒ dY(f(x), f(y)) < ε

Published on 28 Feb 2023 - 22:29

score 59 · Answer 5 · 2023-03-02 23:03:07

59

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How do I find an $N$ such that for $n > N$, the following term is less than $\epsilon$?

Published on 02 Mar 2023 - 23:03

score 123 · Answer 6 · 2026-03-25 21:00:11

123

Views

Piecewise limit does not exist proof

Published on 25 Mar 2026 - 21:00

score 306 · Answer 7 · 2023-03-04 11:33:48

306

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Difficulties with estimation of epsilon-delta limit proof

Published on 04 Mar 2023 - 11:33

score 132 · Answer 8 · 2023-03-04 18:11:58

132

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How do we prove that $\lim_{x\to+\infty}\frac{x+1}{x^{2}}$ converges to $0$ by the definition?

Published on 04 Mar 2023 - 18:11

score 53 · Answer 9 · 2023-03-04 21:01:53

53

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Prove that if $\lim_{x\to 0} f(x) = L \neq 0$ and $\lim_{x\to 0} g(x)$ does not exist, then $\lim_{x\to 0} f(x)g(x)$ does not exist.

Published on 04 Mar 2023 - 21:01

score 35 · Answer 10 · 2026-03-27 01:46:57

35

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Is this the right way to think of epsilon-delta proofs when $d = \min(c, e(c))$?

Published on 27 Mar 2026 - 1:46

score 126 · Answer 11 · 2023-03-05 01:27:10

How to specify delta in a non-symmetric way (in an epsilon-delta proof)? Or what is the strategy that proves $\sqrt{x} \to \sqrt{a}$ when $x \to a$?

score 88 · Answer 12 · 2023-03-08 11:58:28

88

Views

Must $ \epsilon$-$\delta$ proof end up with a $\epsilon$

Published on 08 Mar 2023 - 11:58

score 50 · Answer 13 · 2023-03-09 02:21:21

50

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Does $|x-1|<\delta\implies |f(x)-4|<\epsilon$ and so $\lim_{x\to 1} f(x)$ exists?

Published on 09 Mar 2023 - 2:21

score 68 · Answer 14 · 2023-03-12 11:53:56

68

Views

Why are these two $\varepsilon$-$\delta$ definitions of the limit of a function at a point equivalent?

Published on 12 Mar 2023 - 11:53

score 44 · Answer 15 · 2023-03-14 03:38:06

44

Views

Question on logic of epsilon and delta proof

Published on 14 Mar 2023 - 3:38

List Question

Can we rephrase Epsilon-delta definition?

Proving a limit exists by using epsilon delta definition

$\forall x$ versus $\exists x$ in the definition of limit

Let f:(X, $d_X$) → (Y, $d_Y$). Show f continuous if and only if ∀x ∈ X and ∀ε > 0, exists δ > 0 such that ∀y ∈ X, dX(x , y) < δ ⇒ dY(f(x), f(y)) < ε

How do I find an $N$ such that for $n > N$, the following term is less than $\epsilon$?

Piecewise limit does not exist proof

Difficulties with estimation of epsilon-delta limit proof

How do we prove that $\lim_{x\to+\infty}\frac{x+1}{x^{2}}$ converges to $0$ by the definition?

Prove that if $\lim_{x\to 0} f(x) = L \neq 0$ and $\lim_{x\to 0} g(x)$ does not exist, then $\lim_{x\to 0} f(x)g(x)$ does not exist.

Is this the right way to think of epsilon-delta proofs when $d = \min(c, e(c))$?

How to specify delta in a non-symmetric way (in an epsilon-delta proof)? Or what is the strategy that proves $\sqrt{x} \to \sqrt{a}$ when $x \to a$?

Must $ \epsilon$-$\delta$ proof end up with a $\epsilon$

Does $|x-1|<\delta\implies |f(x)-4|<\epsilon$ and so $\lim_{x\to 1} f(x)$ exists?

Why are these two $\varepsilon$-$\delta$ definitions of the limit of a function at a point equivalent?

Question on logic of epsilon and delta proof

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