Strongly proper sub-APS

From Apstheory

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	Any [[proper sub-APS|proper]] [[saturated sub-APS]] is strongly proper.		Any [[proper sub-APS|proper]] [[saturated sub-APS]] is strongly proper.
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-	[[Category: Terminology local to the wiki]]
-	[[Category: Set-theoretic sub-APS properties]]
-	[[Category: sub-APS properties]]

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Current revision as of 23:20, 25 January 2007

This article defines terminology that is local to the wiki. For its use outside the wiki, please give full definitions

This article describes a property that can be evaluated for a sub-APS of an APS and uses only set-theoretical properties

[edit] Definition

[edit] Symbol-free definition

A sub-APS is termed strongly proper in the APS if there are infinitely many indices for which the sub-APS member is a proper subset of the APS member.

[edit] Definition with symbols

A sub-APS Failed to parse (Can't write to or create math temp directory): H

of an APS Failed to parse (Can't write to or create math temp directory): G
is termed strongly proper if there are infinitely many indices Failed to parse (Can't write to or create math temp directory): n
for which Failed to parse (Can't write to or create math temp directory): H_n
is a proper subset of Failed to parse (Can't write to or create math temp directory): G_n

.

Any proper saturated sub-APS is strongly proper.