## jueves, 25 de octubre de 2012

### Extra points

what will be done with this problem is to know if a group with the theory of gruop.

Problem to solve

2 + 3 = 10
8 + 4 = 96
7 + 2 = 63
6 + 5 = 66
9 + 5 = ?

Solution to problem:

2 + 3 = 10 (2+3=5(2))
8 + 4 = 96 (8+4=12(8))
7 + 2 = 63 (7+2=9(7))
6 + 5 = 66 (6+5=11(6))
9 + 5 = ? (9+5=14(9))

Result:
9 + 5 = 126

Associativity:
$a \circ (b \circ c)=(a \circ b) \circ c, \forall a,b,c \in G$

this point is not met and the order matters of factors in this problem, the result is not the same.

Neutral element:

$\exists e \in G : e \circ a=a \circ e=a$

This time this point is not met because the result set given in the problem are not equal to the sum of any factor.

Symmetrical element:
$\forall a \in G\quad \exists a^{-1} \in G : a\circ a^{-1}=a^{-1} \circ a=e$

At this point I think it's obviously not apply to what is being done on the problem

Group:
A group is a set G which has defined an internal composition law that satisfies the above axioms.

Then this, problem is not a group because don´t meets with some requeriments, do as explain his definition.

This is of wikipedia now i try explain of the pdf of Elisa Schaeffer:

Identity:
e°g = g°e = g

this is not true since we have to
a(a + b) = c
a(a + e) is different from c

Reverse:
so if there is no identity, can not be reversed and also used "e"

Associativity:
the associativity is not because we
a (a + b) = c
Not the same that
b (b + a) = c

Closing:
this point is correct because it says that if g ° h belongs to G
And that g, h belongs to G
Are integers
If you multiply
You get a whole number

Then we come to the same conclusion on this problem is not a group

Well, I hope that the result is the desired and sorry for my bad english.

References: