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April 8th, 2017, 01:59 AM  #1 
Newbie Joined: Jul 2012 Posts: 5 Thanks: 0  How summing groups of elements?
Summing groups of elements is probably one of the mathematical things that people apply the most. But I wonder how this is done mathematically in a correct way. Examples:
Notes:
So which mathematical technique is used to sum groups in a in a correct way? Thanks in advance! 
April 8th, 2017, 12:16 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,790 Thanks: 922 
I would just use vector addition. Each element of the vector corresponds to the number of a unique type of fruit or whatever. You can make the elements mean whatever you like as long as they are unique descriptors. letting $v=(apples, pears, bananas)$ we have $(1,2,0)+(2,0,1) = (3,2,1)$ $(1,0,0)+(1,0,0) = (2,0,0)$ etc. 
April 9th, 2017, 11:02 PM  #3 
Newbie Joined: Jul 2012 Posts: 5 Thanks: 0 
Thanks! Vector addition is indeed a way (maybe the only) to do this. Although I have some doubts about the axiom about the existence of an inverse element (required for a vector space). I can imagine that some mathematicians will say that they have never seen a negative apple. Unless of course that removing an apple can be considered as inverse element. 

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elements, groups, summing 
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