When trying to prove thar the limit of a seq is unique, i saw in my notes tt for episilion >0, la-bl>2episilion assuming that a and b r the limits of the seq.
Then from here, why does it mean that la-bl =0?
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If you mean then we get equality because can be arbitrarily small. If a and be were not equal you could choose small enough to break the inequality. Note that any constant multiple of would work just as well.
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