Talk:Extremal length: Difference between revisions

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Need to add credit to inventer(s) of extremal length Oded (talk) 17:44, 20 April 2008 (UTC)[reply]

Dubious: $inf h (s) = \infty$

$h (s)$ is not even defined when $s = 0$ .
Taking the juxtaposition to mean a quotient, it means that the infimum is $\infty$ , i.e. the set is empty.

BTW the proof is too long and complicated for Wikipedia IMHO anyway. --Yecril (talk) 18:01, 18 September 2008 (UTC)[reply]

The Introduction is missing information

This sentence appears in the Introduction:

"More specifically, suppose that $D$ is an open set in the complex plane and $\Gamma$ is a collection of paths in $D$ and $f:D\to D'$ is a conformal mapping."

This refers to D (an open set in the plane) and also to D' — which it never defines. It needs to state what D' is. Is it another open set in the plane? If so, readers should not need to guess.

The next sentence is this:

"Then the extremal length of $\Gamma$ is equal to the extremal length of the image of $\Gamma$ under $f$ ."

This defines extremal length in terms of extremal length! In mathematics we generally avoid recursive definitions. I hope someone knowledgeable on this subject can fix this.50.203.182.230 (talk) 14:44, 1 June 2020 (UTC)[reply]

@@ Line 11: / Line 11: @@
 --[[User:Yecril|Yecril]] ([[User talk:Yecril|talk]]) 18:01, 18 September 2008 (UTC)
-== The introduction is missing information ==
+== The Introduction is missing information ==
+This sentence appears in the '''Introduction''':
-The '''Introduction''' refers to D (an open set in the plane) and also to D' — which it never defines. It needs to state what D' is. Is it another open set in the plane? If so, readers should not need to guess.[[Special:Contributions/50.203.182.230|50.203.182.230]] ([[User talk:50.203.182.230|talk]]) 14:39, 1 June 2020 (UTC)
+"''More specifically, suppose that <math>D</math> is an open set in the [[complex plane]] and <math>\Gamma</math> is a collection of paths in <math>D</math> and <math>f:D\to D'</math> is a conformal mapping.''"
+This refers to D (an open set in the plane) and also to D' — which it never defines. It needs to state what D' is. Is it another open set in the plane? If so, readers should not need to guess.
+The next sentence is this:
+"''Then the extremal length of <math>\Gamma</math> is equal to the extremal length of the image of <math>\Gamma</math> under <math> f</math>.''"
+This defines extremal length in terms of extremal length! In mathematics we generally avoid recursive definitions. I hope someone knowledgeable on this subject can fix this.[[Special:Contributions/50.203.182.230|50.203.182.230]] ([[User talk:50.203.182.230|talk]]) 14:44, 1 June 2020 (UTC)

Revision as of 14:45, 1 June 2020

Dubious: inf h(s) = ∞

The Introduction is missing information

Dubious: $inf h (s) = \infty$