Question Number 183181 by sciencestudent last updated on 22/Dec/22
$${prove}\:{that}\:\frac{\mathrm{0}}{\mathrm{0}}=\mathrm{1} \\ $$
Commented by Gazella thomsonii last updated on 22/Dec/22
$${prove}\:{that}\:\frac{\mathrm{0}}{\mathrm{0}}=\mathrm{1} \\ $$$$\mathrm{False} \\ $$
Answered by alephzero last updated on 22/Dec/22
$$\frac{\mathrm{0}}{\mathrm{0}}\:\mathrm{is}\:\mathrm{undefined}. \\ $$$$\mathrm{But}\:\mathrm{we}\:\mathrm{can}\:\mathrm{suppose}\:\mathrm{that}\:\mathrm{if}\:\frac{{x}}{{x}}\:=\:\mathrm{1}, \\ $$$$\mathrm{then}\:\frac{\mathrm{0}}{\mathrm{0}}\:=\:\mathrm{1}. \\ $$$$\mathrm{Also}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}}{{x}}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left({x}\right)'}{\left({x}\right)'}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}1}\:=\:\mathrm{1} \\ $$$$\mathrm{But}\:\mathrm{also}\:\mathrm{we}\:\mathrm{can}\:\mathrm{define}\:\frac{\mathrm{0}}{\mathrm{0}}\:\mathrm{as}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{0}}{{x}} \\ $$$$\mathrm{which}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{0},\:\mathrm{and}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}}{\mathrm{0}}\:\mathrm{which} \\ $$$$\mathrm{is}\:\mathrm{undefined}. \\ $$
Answered by BaliramKumar last updated on 23/Dec/22
$${prove}\:{that}\:\frac{\mathrm{0}}{\mathrm{0}}=\mathrm{1} \\ $$$$ \\ $$$$\frac{\mathrm{0}}{\mathrm{0}}\:=\:\frac{{x}−{x}}{{x}−{x}}\:=\:\frac{{x}\cancel{\left(\mathrm{1}−\mathrm{1}\right)}}{{x}\left(\cancel{\mathrm{1}−\mathrm{1}\right)}}\:=\:\frac{{x}}{{x}}\:=\:\mathrm{1} \\ $$$$ \\ $$$$\frac{\mathrm{0}}{\mathrm{0}}\:=\:\frac{\pi−\pi}{\mathrm{1}−\mathrm{1}}\:=\:\frac{\pi\cancel{\left(\mathrm{1}−\mathrm{1}\right)}}{\cancel{\left(\mathrm{1}−\mathrm{1}\right)}}\:=\:\:\pi \\ $$$$ \\ $$$$\frac{\mathrm{0}}{\mathrm{0}}\:{is}\:{undefind}\:{so}\:\frac{\mathrm{0}}{\mathrm{0}}\:{can}\:{be}\:{any}\:{numbers} \\ $$
Commented by sciencestudent last updated on 23/Dec/22
$${thanks} \\ $$