Hello I'm new to this forum.
I've looked at Grandi's series:
S = 1 - 1 + 1 - 1 + 1 ...
If you add brackets, you can get two different result:
S = (1 - 1) + (1 - 1) + (1 - 1) + ... = 0
S = 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + ... = 1
and you can also derive the equation:
1 - S = S
My question is, instead of saying S = 0.5, can't simply say S is either one or zero depending on context (S = <0|1>)?
You could still solve the equation 1 - S = S:
1 - S1<0|1> = S2<0|1>
If you choose a value for one instance of S the other instance gets fixed:
S1 = 0 -> S2 = 1: 1 - 0 = 1
S1 = 1 -> S2 = 0: 1 - 1 = 0