anonymous
  • anonymous
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)
Mathematics
chestercat
  • chestercat
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amistre64
  • amistre64
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.
amistre64
  • amistre64
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.
amistre64
  • amistre64
what about division? 12/4 = 3 4/12 = 1/3 ...division is not commutative :)

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amistre64
  • amistre64
associative is just the larger version of commutative, and it deals with associating numbers together...
amistre64
  • amistre64
(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
amistre64
  • amistre64
(4/2)/2 = 2/2 = 1 4/(2/2) = 4/1 = 4 ...division is NOT associative
amistre64
  • amistre64
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)
amistre64
  • amistre64
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
amistre64
  • amistre64
closure? got no idea on that one ;)
anonymous
  • anonymous
Thank you!
amistre64
  • amistre64
youre welcome... i hope it helped out :)
amistre64
  • amistre64
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

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