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I am not treating infinity as a finite number. And I am not ever assuming we ran out of marbles, even though we may have lost some.
Think about this:
Take the equation y=(1-x)/(1-x)
In this case, the limit as x->1 exists and is 1, but the value of y is undefined at x=1 (0/0).
This is one of the easiest ways I can express the difference between approaching a value, and actually reaching it.
Bear in mind that I am no expert, and I am trying to illustrate a much more subtle problem with simple examples (between beers).
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"Socialism is a philosophy of failure, the creed of ignorance, and the gospel of envy, its inherent virtue is the equal sharing of misery." - Winston Churchill
"All men dream: but not equally. Those who dream by night in the dusty recesses of their minds wake in the day to find that it was vanity: but the dreamers of the day are dangerous men, for they may act out their dream with open eyes, to make it possible." Seven Pillars of Wisdom, T.E. Lawrence
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