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Let [math]G[/math] be a non empty set with binary operation [math]+[/math]. G is said to be a Group if the following conditions are satisfied:

  1. [math]G[/math] is closed with respect to [math]+[/math] i.e. if [math]a,b\in G \Rightarrow a+b\in G[/math]
  2. Existance of Identity element i.e.Ther exists [math]e\in G[/math] such that for any [math]a\in G, a+e=a=e+a[/math]
  3. Existance of Inverse i.e. for any [math]a\in G,[/math] there exists [math]b\in G[/math] such that [math] a+b=e=b+a [/math]


[math]\Re[/math] Set of real numbers form a Group with respect to addition"+".