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.99999999... converges to 1, and for all real-world applications is equal to 1.
However, there is the question of whether 1/infinity (the number that .9999... would have to be added to to equal 1) is equal to zero or not is really the point we are debating.
I say that since the numerator is a non-zero term, that it is not actually equal to zero, no matter how large the denominator is.
Of course, since 1/infinity isn't a real number (since infinity is also not a real number), it just gets messy.
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