Thank you for the help, Euge ...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.
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.
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.
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).
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.
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.