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let-set-S-R-let-nS-R-R-R-n-sets-of-R-n-Z-is-S-lt-nS-what-if-n-S-




Question Number 11145 by FilupS last updated on 14/Mar/17
let set S=R  let nS={R, R, ..., R_(n sets of R) }         n∈Z^+   is ∣S∣<∣nS∣?     what if n=∣S∣?
$$\mathrm{let}\:\mathrm{set}\:{S}=\mathbb{R} \\ $$$$\mathrm{let}\:{nS}=\left\{\underset{{n}\:\mathrm{sets}\:\mathrm{of}\:\mathbb{R}} {\mathbb{R},\:\mathbb{R},\:…,\:\mathbb{R}}\right\}\:\:\:\:\:\:\:\:\:{n}\in\mathbb{Z}^{+} \\ $$$$\mathrm{is}\:\mid{S}\mid<\mid{nS}\mid? \\ $$$$\: \\ $$$$\mathrm{what}\:\mathrm{if}\:{n}=\mid{S}\mid? \\ $$
Commented by prakash jain last updated on 15/Mar/17
S is noy countable.  ∣nS∣=1 since duplicate elements are removed.  nS is a set of sets.
$$\mathrm{S}\:\mathrm{is}\:\mathrm{noy}\:\mathrm{countable}. \\ $$$$\mid{nS}\mid=\mathrm{1}\:\mathrm{since}\:\mathrm{duplicate}\:\mathrm{elements}\:\mathrm{are}\:\mathrm{removed}. \\ $$$${n}\mathrm{S}\:{is}\:{a}\:{set}\:{of}\:{sets}. \\ $$

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