Question Number 4950 by madscientist last updated on 25/Mar/16
$${what}\:{is}\:{a}\:{whole}\:{divided}\:{by}\:{diffrent}\:{amouts} \\ $$$${infinitly}\:{what}\:{does}\:{it}\:{sooner}\:{or}\:{later}\:{equal}? \\ $$
Commented by prakash jain last updated on 25/Mar/16
$$\mathrm{Successive}\:\mathrm{division}\:\mathrm{by}\:\mathrm{0}<{x}<\mathrm{1} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{{x}^{{n}} }\rightarrow\infty \\ $$$$\mathrm{Successive}\:\mathrm{division}\:\mathrm{by}\:\mathrm{1}\:\mathrm{infinitely}=\mathrm{1} \\ $$$$\mathrm{Successive}\:\mathrm{division}\:\mathrm{by}\:{x}\:>\mathrm{1}\:\mathrm{infinitely}=\mathrm{0} \\ $$$$\mathrm{succesive}\:\mathrm{division}\:{x}<−\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{succesive}\:\mathrm{division}\:−\mathrm{1}\leqslant{x}\leqslant\mathrm{0}\:\:\mathrm{indeterminate} \\ $$