- #1
Mr Davis 97
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I'm looking at the quantity ##\displaystyle 1 - \frac{N}{n}##, and trying to prove that it is greater than ##1/2##, given that ##n> N##. I thought that since ##\lim_{n \to \infty} 1 - \frac{N}{n} = 1##, we could use the definition of convergence to get this inequality, for suitable ##\epsilon##. For example, from the definition of convergence we can see that ##|(1 - N/n) - 1| < \epsilon## which implies ##N/n < \epsilon##, and so ##1-N/n > 1- \epsilon##. So if we let ##\epsilon = 1/2##, we get our result. Is that how I would do it?