The discussion revolves around the properties of a group law defined by the operation a*b=eln(a)*ln(b) in the context of algebraic structures. Participants are exploring whether this group law is associative and commutative, as well as the existence of an identity element.
Participants do not reach a consensus on the properties of the group law. While some believe they have found evidence for commutativity, others argue that more rigorous proof is necessary, indicating ongoing disagreement and uncertainty.
Limitations include the reliance on specific numerical examples rather than a general proof, and the need for clearer definitions and steps to demonstrate the properties of the group law.
naoufelabs said:Please I have a problem with natural log for group set as follow:
a*b=eln(a)*ln(b)
1- Show that the group law * is associative and commutative
2- Show that the group law * accept an element e (Identity element)
Thank you !
naoufelabs said:I tested with Maple e^ln(a)*ln(b), then the result is a^ln(b).
so I tested with 2 different numbers, example:
3^ln(2) = 2^ln(3) ==> Gives the same result.
So I found that the e^ln(a)*ln(b) is commutative.
naoufelabs said:I tested with Maple e^ln(a)*ln(b), then the result is a^ln(b).
so I tested with 2 different numbers, example:
3^ln(2) = 2^ln(3) ==> Gives the same result.
So I found that the e^ln(a)*ln(b) is commutative.