Wotzdorfg

2021-02-13

1. Show that sup $\{1-\frac{1}{n}:n\in N\}=1\{1-\frac{1}{n}:n\in N\}=\frac{1}{2}$ . If $S{\textstyle \phantom{\rule{0.222em}{0ex}}}=\{\frac{1}{n}-\frac{1}{m}:n,m\in N\}S{\textstyle \phantom{\rule{0.222em}{0ex}}}=\{\frac{1}{n}-\frac{1}{m}:n,m\in N\},f\in d\in fS{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\supset S.end\left\{tab\underset{\u2015}{a}r\right\}$

Aniqa O'Neill

Skilled2021-02-14Added 100 answers

Let

N0

This contradicts that aa is not an uper bound of SS. Hence 11 is the least upper bound of SS consequently

Now since

Similarly we can prove that