- #1
- 7,643
- 1,599
What does the symbol ##\supset## mean as used in equations (3.1) and (3.2) of
https://arxiv.org/pdf/1701.07427.pdf
https://arxiv.org/pdf/1701.07427.pdf
The symbol "##\supset##" is used to represent the logical operator "implies" in mathematical equations. It indicates that the expression on the left side of the symbol implies the expression on the right side.
In Eqs. 3.1 & 3.2, the symbol "##\supset##" is used to show the relationship between two mathematical expressions. It is typically used when describing conditional statements, where the first expression (before the symbol) must be true in order for the second expression (after the symbol) to also be true.
Some other commonly used symbols in mathematical equations include "##\forall##" for "for all," "##\exists##" for "there exists," "##\in##" for "belongs to," "##\rightarrow##" for "implies," and "##\leftrightarrow##" for "if and only if."
While both symbols are used to represent logical implications in mathematical equations, the "##\supset##" symbol is typically used for conditional statements, where the first expression must be true in order for the second expression to also be true. The "##\rightarrow##" symbol, on the other hand, is used for material implications, where the truth of the first expression guarantees the truth of the second expression.
Yes, the "##\supset##" symbol can also be used in other logical contexts, such as in propositional logic and set theory. In these contexts, it can have different meanings and represent different logical operations, such as implication, subset, or superset. It is important to always consider the specific context in which the symbol is being used to understand its meaning.