Question

I dont understand the 12 hr clock system as a gommunative group. can anyone help me? There also other groups (closure,associative,idenity,invers and communative property)

Answer 1

commutative means to travel, to commute from one place to another;

groups are commutative if you can switch them around and still retain the same value, for example:

-5 + 8 = 3

8 - 5 = 3 ...... addition is commutative.

Answer 2

lets try multiplication:

4(-9) = -36

-9(4) = -36 ....... muliplication is ALSO commutative

we can switch the position of the numbers and still retain the value.

Answer 3

what about division?

12/4 = 3

4/12 = 1/3 ...division is not commutative :)

Answer 4

associative is just the larger version of commutative, and it deals with associating numbers together...

Answer 5

(4+3)-6 = 7-6 = 1

4+(3-6) = 4+(-3) = 1 addition is associative...

(3*2)*5 = 6(5) = 30

3*(2*5) = 3(10) = 30 ....multiplication is associative

Answer 6

(4/2)/2 = 2/2 = 1

4/(2/2) = 4/1 = 4 ...division is NOT associative

Answer 7

identity is like looking in the mirror... you see your own reflection.

the additive identity is "0"

4+0 = 4; -2+0 = -2; (3/4) - 0 = (3/4)

the multiplicative identity is "1"

2(1) = 2 ; 2365(1) = 2365 ; (3/5)(1) = (3/5)

Answer 8

an inverse is the reverse of the identity.......

for example:

a * a^-1 = 1

a +(-a) = 0

the additive inverse is the opposite of the number/object. so that adding them together =0

the muliplication inverse is the reciprocal of a number.

4(1/4) = 1

Answer 9

closure? got no idea on that one ;)

Answer 10

Thank you!

Answer 11

youre welcome... i hope it helped out :)

Answer 12

I would say that the clock system is commutative because it doesnt matter how you add the hours together, you get the same results..... but I am not up to date on "group" theory