If P(n) is a sentential formula depending on a variable n ranging in a set of real numbers, the sentence P(n) for every sufficiently large n means exists N such that P(n) for all n>N. An example is the proposition 1/n^2<0.0001 for every sufficiently large n, which is true, since the inequality is fulfilled for n>100. The statement can also be rephrased as follows: the terms of the sequence {1/n^2}_(n = 1)^∞ become eventually smaller than 0.0001.
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