Mini algebra 1

Abstract Algebra is my favorite Math categories; it totally opened a new world for me. 2+2 is not necessarily equal to 4 anymore; we could not take a+b = b+ a for grant ; logos or pictures have mathematical meaning presentations…..

The foundation of Contemporary Algebra is built on the concept of Group. Some math genius got so bored so they started to look at the algebraic structures in different Set, and they found some interesting facts:

For Integers, Z under addition, we have

  1. a+0=a for a in Z
    e.g.  1+0=1, 2+0=2
  2. For every a in Z, there is a -a, such that, a+(-a) =0
    e.g. 1+(-1) =0, 100+ (-100)=0
  3. (a+b)+c= a+ (b+c)
    e.g.  (1+2)+3= 1+(2+3) ….

But some of these properties will not hold if it is integers under minus, e.g. (1-2)-3= -4 is not equal to 1-(2-3)=2

After the studying of the algebriac structure of numbers, mathematicians reached the definition of Group.

marijana1 / Pixabay

A Group is a set of elements closed under a binary operation with 3 conditions:

  1. Every group contains a unique identity.
    n+e=n
  2. Every element in the group has an inverse.
    a+ (-a) = e
  3. The operation is associative.
    a+(b+c)= (a+b)+c

Next time, we will give some example of Group ….

 

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