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I-m-curious-about-your-response-to-this-Where-is-the-mistake-0-0-100-100-100-100-0-0-10-2-10-2-10-10-10-0-0-10-10-10-10-10-10-10-0-0-10-10-10-0-0-20-10

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Question Number 5926 by FilupSmith last updated on 05/Jun/16
I′m curious about your response to this Where is the mistake: (0/0)=((100−100)/(100−100)) (0/0)=((10^2 −10^2 )/(10(10−10))) (0/0)=(((10−10)(10+10))/(10(10−10))) (0/0)=(((10+10))/(10)) (0/0)=((20)/(10)) (0/0)=2
$$\mathrm{I}'\mathrm{m}\:\mathrm{curious}\:\mathrm{about}\:\mathrm{your}\:\mathrm{response}\:\mathrm{to}\:\mathrm{this} \\ $$$$ \\ $$$$\mathrm{Where}\:\mathrm{is}\:\mathrm{the}\:\mathrm{mistake}: \\ $$$$\frac{\mathrm{0}}{\mathrm{0}}=\frac{\mathrm{100}−\mathrm{100}}{\mathrm{100}−\mathrm{100}} \\ $$$$\frac{\mathrm{0}}{\mathrm{0}}=\frac{\mathrm{10}^{\mathrm{2}} −\mathrm{10}^{\mathrm{2}} }{\mathrm{10}\left(\mathrm{10}−\mathrm{10}\right)} \\ $$$$\frac{\mathrm{0}}{\mathrm{0}}=\frac{\left(\mathrm{10}−\mathrm{10}\right)\left(\mathrm{10}+\mathrm{10}\right)}{\mathrm{10}\left(\mathrm{10}−\mathrm{10}\right)} \\ $$$$\frac{\mathrm{0}}{\mathrm{0}}=\frac{\left(\mathrm{10}+\mathrm{10}\right)}{\mathrm{10}} \\ $$$$\frac{\mathrm{0}}{\mathrm{0}}=\frac{\mathrm{20}}{\mathrm{10}} \\ $$$$\frac{\mathrm{0}}{\mathrm{0}}=\mathrm{2} \\ $$
Commented by FilupSmith last updated on 05/Jun/16
My assumtion is that 10−10 can not be factored out (divide by zero). i.e. ((0a)/(0b))≠(a/b)
$$\mathrm{My}\:\mathrm{assumtion}\:\mathrm{is}\:\mathrm{that}\:\mathrm{10}−\mathrm{10}\:\mathrm{can}\:\mathrm{not} \\ $$$$\mathrm{be}\:\mathrm{factored}\:\mathrm{out}\:\left(\mathrm{divide}\:\mathrm{by}\:\mathrm{zero}\right). \\ $$$$\mathrm{i}.\mathrm{e}.\:\:\frac{\mathrm{0}{a}}{\mathrm{0}{b}}\neq\frac{{a}}{{b}} \\ $$
Commented by Yozzii last updated on 05/Jun/16
(0/0) is undefined.
$$\frac{\mathrm{0}}{\mathrm{0}}\:{is}\:{undefined}. \\ $$
Commented by FilupSmith last updated on 05/Jun/16
yes, that was what I was getting at
$$\mathrm{yes},\:\mathrm{that}\:\mathrm{was}\:\mathrm{what}\:\mathrm{I}\:\mathrm{was}\:\mathrm{getting}\:\mathrm{at} \\ $$
Commented by 123456 last updated on 05/Jun/16
(x/y)=z⇒x=yz x=0,y=0⇒0=0z∀z x≠0,y=0⇒0≠x=0z=0 (impossible ∀z)
$$\frac{{x}}{{y}}={z}\Rightarrow{x}={yz} \\ $$$${x}=\mathrm{0},{y}=\mathrm{0}\Rightarrow\mathrm{0}=\mathrm{0}{z}\forall{z} \\ $$$${x}\neq\mathrm{0},{y}=\mathrm{0}\Rightarrow\mathrm{0}\neq{x}=\mathrm{0}{z}=\mathrm{0}\:\left(\mathrm{impossible}\:\forall{z}\right) \\ $$

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