what is the difference between an equal sign with another line above it and an equal sign with a triangle above it.
I was alway taught that the three lines symbolized identity
and that the equal sign with a traingle above it signified definition
when would you use the three lines instead of the equal sign with a traingle above it
right now I see them as being interchangeable which I think might be wrong...
thanks
The symbol you are referring to as "an equal sign with another line above it" is called a "triple equal sign" or "triple bar." It is often used to indicate strict equality or identity between two mathematical objects. The symbol you described as "an equal sign with a triangle above it" is commonly called a "defining equals sign" or "definition symbol."
The triple equal sign is typically used in mathematics and computer science to assert that two objects or expressions are exactly the same, without any variations or exceptions. It indicates that the two sides of the equality are interchangeable and have the same attributes in all circumstances. For example, if A = B, it means that A and B are equivalent in every possible way.
On the other hand, the defining equals sign or definition symbol is used to define or introduce a new term or concept. It signifies that the expression on the left-hand side is being defined as the expression on the right-hand side. This symbol is often used in mathematical proofs or when establishing a new notation or concept. For example, if we define A ≡ B, it means that we are defining A to be the same as B.
While these symbols may have different usages and connotations, it is important to note that their specific meanings can vary depending on the context and field of study. It's always a good idea to consult the specific guidelines or definitions provided in the literature or resources you are working with.
In summary, the triple equal sign represents strict equality, indicating that two objects are exactly the same, while the defining equals sign denotes a definition, introducing a new term or concept. It is crucial to understand the specific definitions and conventions within your particular area of study to ensure accurate usage.