Fix mathematically incorrect statements about empty sets in set documentation

[Copilot]

Problem

The documentation for multiple set types contained mathematically incorrect statements about empty sets:

1. In IsProperSupersetOf methods:

   An empty set is a proper superset of any other collection.

2. In IsProperSubsetOf methods:

   An empty set is a proper subset of any other collection.

Both statements violate basic set theory principles.

Solution

Corrected all statements to align with mathematical set theory:

An empty set is a subset of any other collection.

Mathematical Background

In set theory:

• An empty set (∅) contains no elements
• A proper superset of set B is a set A that contains all elements of B and has at least one additional element
• A proper subset of set B is a set A that contains only elements from B and has fewer elements than B
• Since an empty set has no elements, it cannot be a proper superset or proper subset of any set
• However, an empty set is a subset of every set, including itself (but not a proper subset of another empty set)

Change Details

Fixed incorrect statements in the following files:

1. ImmutableSortedSet`1.xml:

   • IsProperSubsetOf remarks (line 627)
   • IsProperSupersetOf remarks (line 682)

2. HashSet`1.xml:

   • IsProperSubsetOf remarks (line 1597)
   • IsProperSupersetOf remarks (line 1679)

3. SortedSet`1.xml:

   • IsProperSubsetOf remarks (line 1396)
   • IsProperSupersetOf remarks (line 1465)

4. ISet`1.xml:

   • IsProperSubsetOf remarks (line 288)
   • IsProperSupersetOf remarks (line 349)

All changes remove the word "proper" from the empty set statements to correctly reflect that an empty set is a subset (not a proper subset or proper superset) of all sets.

Impact

Corrects the mathematical explanations without affecting functionality. The method behavior remains unchanged - the documentation now accurately describes what the methods return.

Fixes #11853

Original prompt

---

This section details on the original issue you should resolve

<issue_title>Mathematically incorrect statement, probably a typo/copy-paste error</issue_title>
<issue_description>### Type of issue

Typo

Description

The remarks section says

An empty set is a proper superset of any other collection.

It should say

An empty set is a subset of any other collection.

Note, not a proper subset.

Page URL

https://learn.microsoft.com/en-us/dotnet/api/system.collections.immutable.immutablesortedset-1.ispropersupersetof?view=net-8.0

Content source URL

https://github.com/dotnet/dotnet-api-docs/blob/main/xml/System.Collections.Immutable/ImmutableSortedSet`1.xml

Document Version Independent Id

6db3f697-2a43-407f-bb31-9b103716008c

Platform Id

b2b81307-57ac-f3a2-40a2-2c61472b04c9

Article author

@dotnet-bot</issue_description>

Comments on the Issue (you are @copilot in this section)

@eiriktsarpalis Sounds about right.

Fixes #11853

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[PranavSenthilnathan]

@copilot Can you update the other sets as well (ISet, HashSet, etc.)?

[Copilot]

Updated all set types (ISet, HashSet, SortedSet) with the same fix in commit 65142cb.

[PranavSenthilnathan]

This statement ("An empty set is a proper subset of any other collection.") is also wrong. Update this and other occurrences (e.g. in ISet, HashSet, etc.).

[Copilot]

Fixed the IsProperSubsetOf statements in all affected files (ImmutableSortedSet, ISet, HashSet, SortedSet). Changed "proper subset" to "subset" in commit 65142cb.