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If I remember correctly, it has something to do with the way that sums/series work when dealing with infinities. I don't remember exactly how it reduces, but I remember my mind being moderately blown the first time it was explained to me.
Now, my attempt, as I think about right now, would be to reduce it to an infinite series of the sum of one minus one:
(1 - 1) + (1 - 1) + (1 - 1) + ....
Which would of course reduce to 0 + 0 + 0 + ... = 0...
I know this is wrong (because I've not correctly applied whatever rule leads to the 1/2 answer,) but from a straightforward idiot's logic approach, it makes sense.