Subset of - BUT - not equal to ....

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In summary, "Subset of - BUT - not equal to ...." refers to a relationship between two sets where one set is a subset of the other but is not equal to it. This relationship is represented mathematically as A ⊂ B, where A is the first set and B is the second set. An example of this relationship is the sets A = {1,2,3} and B = {1,2,3,4}. This relationship is different from "proper subset of" because it allows for the possibility of the two sets being equal. This concept is significant in mathematics for defining the hierarchy of sets and their relationships.
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In Paolo Aluffi's proof of the Jordan-Holder Theorem he uses a symbol indicating a subset of a group ... BUT ... not equal to the group ... as in the following, between say \(\displaystyle G_0\) and \(\displaystyle G_1\) ...
View attachment 4913Can someone help with the Latex code for the symbol ... ...

Peter
 
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  • #2
The code you're looking for is \supsetneq, which produces $\supsetneq$. So you'll be able to write $G_0 \supsetneq G_1$ as in the book.
 
  • #3
Euge said:
The code you're looking for is \supsetneq, which produces $\supsetneq$. So you'll be able to write $G_0 \supsetneq G_1$ as in the book.
Thank you for the help, Euge ...
 

FAQ: Subset of - BUT - not equal to ....

What does "Subset of - BUT - not equal to ...." mean?

The phrase "Subset of - BUT - not equal to ...." refers to a relationship between two sets, where one set is a subset of the other but is not equal to it. This means that every element in the first set is also in the second set, but the second set may contain additional elements.

How is this relationship represented mathematically?

In mathematical notation, this relationship can be represented as A ⊂ B, where A is the first set and B is the second set. The symbol ⊂ represents "subset of" and the additional "BUT not equal to" condition is implied.

What is an example of this relationship?

An example of this relationship would be the sets A = {1,2,3} and B = {1,2,3,4}. In this case, A is a subset of B because every element in A (1, 2, and 3) is also in B, but A is not equal to B because B contains an additional element (4).

What is the difference between "subset of - BUT - not equal to" and "proper subset of"?

The difference between these two relationships is that "subset of - BUT - not equal to" allows for the possibility of the two sets being equal, while "proper subset of" does not. In other words, if A is a proper subset of B, then A is always a subset of B, but B may contain additional elements that make it unequal to A.

What is the significance of this relationship in mathematics?

This relationship is important in set theory and other areas of mathematics because it helps define the hierarchy of sets and their relationships to one another. It also allows for more precise descriptions of mathematical concepts and relationships.

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