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For example adding up the infinite time you divide your next step 'reaching' a total of 100%, physically that's impossible, logically it doesn't make much sense to jump from infinite to finite especially when you divide by two never reaching it, but tending towards it..)

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Exactly... it's not physical nor philosophical... so what your confusion lies in the mathematical description of a finite sum to an infinite series. It's math. It doesn't have to make sense, it just has to be mathematically correct.