Language of Binary Operations
What can you say about this? What conclusion can you formulate from this?
Introduction:
We are aware that Algebraic structures focus on investigating sets that are associated
with single operations that satisfy certainly reasonable axioms.
An operation on a set generated structures as the integers together with the single
operation of addition, or invertible 2 x 2 matrices together with the single operation of
matrix multiplication.
Algebraic structures are known as a group.
Let G be a set. A binary operation on G is a function that assigns each ordered pair of
an element of G.
Symbolically, a∗b=G,foralla,b,c∈G.a∗b=G,foralla,b,c∈G.
What is a Group?
A group is a set of elements, with one operation, that satisfies the following properties:
i. the set is closed concerning the operation
ii. the operation satisfies the associative property,
iii. there is an identity element,
What can you say about this? What conclusion can you formulate from this?
Introduction:
We are aware that Algebraic structures focus on investigating sets that are associated
with single operations that satisfy certainly reasonable axioms.
An operation on a set generated structures as the integers together with the single
operation of addition, or invertible 2 x 2 matrices together with the single operation of
matrix multiplication.
Algebraic structures are known as a group.
Let G be a set. A binary operation on G is a function that assigns each ordered pair of
an element of G.
Symbolically, a∗b=G,foralla,b,c∈G.a∗b=G,foralla,b,c∈G.
What is a Group?
A group is a set of elements, with one operation, that satisfies the following properties:
i. the set is closed concerning the operation
ii. the operation satisfies the associative property,
iii. there is an identity element,
