- #1
asap9993
- 19
- 0
Can someone please help me?
Fredrik said:So I think my answer above isn't very appropriate either. I think he's probably asking for the rules of elementary algebra, i.e. the kind of stuff you're allowed to do with variables that represent real numbers. But it looks like the OP has abandoned the thread, so we will probably never know.
Fredrik said:@sponsoredwalk: Sounds like you're going for the definition of "algebra" from universal algebra, and not getting it right. (Why are you only including a binary operation?)
Since the signatures that arise in algebra often contain only function symbols, a signature
with no relation symbols is called an algebraic signature. A structure with such a signature
is also called an algebra; this should not be confused with the notion of an algebra over a
field.
http://en.wikipedia.org/wiki/Structure_(mathematical_logic)
An axiom in algebra is a statement that is accepted as true without needing to be proven. It serves as a starting point for the development of other mathematical concepts.
There are typically 5 or 6 axioms in algebra, depending on the specific system being used. These include the commutative, associative, and distributive properties, as well as the existence of a multiplicative identity and inverse.
Axioms are important in algebra because they allow us to make logical deductions and prove theorems. They provide a solid foundation for the study of algebra and help ensure consistency in mathematical reasoning.
The axioms in algebra are generally accepted as fundamental truths and are not usually changed or modified. However, in some cases, new axioms may be introduced to extend or refine existing systems.
If a mathematical system violates one of the axioms of algebra, then the system may no longer be considered algebraic. This means that certain properties and operations that are typically associated with algebra may not apply in this system.