Math Help - double sum designation question..

the telegan law basically states that the total sum of power is zero.
my prof proved lik this:

we choose a node (a point where more then one currents come together)

and decide that the voltage on that node to be zero.
we designate the voltages on the nodes to be
is the current.



is the number of nodes.[/tex]
is the number of branches.[/tex]

each J that does not exist in the graph will be zero.


because by kcl


my problem iswhen he sums for all nodes
he uses
sign which by me represents multiplication
of the sums

why not ,thus we can know that ist the sum of many similar equations.

but how he did it doesnt represent a sum

The double sum in this case represents a nested sum (if you're familiar with programming, it's like a nested for loop).
In your problem:

means for every iteration of a, we go through all iterations of b. I like to think of it as sort of a series exponentiation.

Formally if we define: and




Will yield different answers. I'm not sure about the actual concepts, I'm not very well versed in physics, but your prof is using the nested case.