# Math Help - Epsilion

1. ## Epsilion

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?

2. If you mean $|a-b|<2\varepsilon$ then we get equality because $\varepsilon$ can be arbitrarily small. If a and be were not equal you could choose $\varepsilon$ small enough to break the inequality. Note that any constant multiple of $\varepsilon$ would work just as well.