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If you add all the numbers .. you will get zero .. cuz every number has a negetive number ..
Is that why zero is the Identity of group under addition ?
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And if you multiply all the numbers , you get 1 .. cuz every number has an inverse .. like 2 has 1/2 ..
Is that why number syatem is a field ? Cuz it satisfies both operations - addition as well as multiplication !
I might be hallucinating :-)
Discussion
1 + (-1) = 0
N + ( -N) = 0
Which means we can all add all the finite numbers it will result to zero ..
Same way
2 * 1/2 = 1
N* 1/N = 1
So if you multiply all the finite numbers ..you will get 1 ..
All unique numbers ..of course ..
And you can't have zero in the operation under multiplication..cuz then it is anyway all zero
In multiplication we are in the integers in the finite field so 1/N isn’t an option - but we can multiply 2 numbers to get 1
Eg in mod(5) 2 * 3 = 1 so 3 is the inverse of 2