Question and Answers Forum

All Questions      Topic List

Geometry Questions

Previous in All Question      Next in All Question      

Previous in Geometry      Next in Geometry      

Question Number 12332 by frank ntulah last updated on 19/Apr/17

$$\mathrm{prove};\left(\frac{0}{0}\right)=2$$

Commented by FilupS last updated on 20/Apr/17

$$\frac{0}{0}=\mathrm{undefined}$$

Commented by FilupS last updated on 20/Apr/17

$$\underset{x\to 0}{\lim }\frac{x}{a}=0(\mid a\mid >0)$$$$\underset{x\to 0}{\lim }\frac{a}{x}=\pm \mathrm{\infty }(\mid a\mid >0)$$$$$$$$\mathrm{by}\mathrm{notation}:$$$$\underset{L\to c}{\lim }\frac{m}{n}=\frac{\underset{L\to c}{\lim }m}{\underset{L\to c}{\lim }n}$$$$\mathrm{or}$$$$\underset{L\to c}{\lim }mn=\left(\underset{L\to c}{\lim }m\right)\left(\underset{L\to c}{\lim }n\right)$$$$$$$$\therefore \underset{x\to 0}{\lim }\frac{x}{x}=\left(\underset{x\to 0}{\lim }x\right)\left(\underset{x\to 0}{\lim }\frac{1}{x}\right)=0\times \mathrm{\infty }=\mathrm{undefined}$$$$\mathrm{because}:$$$$\underset{x\to c}{\lim }\frac{x}{x}=1(\mathrm{\forall }x\ne 0)$$$$\mathrm{if}\mathrm{true}\mathrm{for}x=0,\mathrm{then}1=0\times \mathrm{\infty }$$$$\mathrm{if}0\times \mathrm{\infty }=0\Rightarrow 1=0$$$$\mathrm{if}0\times \mathrm{\infty }=\mathrm{\infty }\Rightarrow 1=\mathrm{\infty }$$$$$$$$\mathrm{both}\mathrm{statements}\mathrm{make}\mathrm{no}\mathrm{sense}$$$$\mathrm{hence}\frac{0}{0}=\mathrm{undefined}$$$$$$$$\mathrm{Edit}:$$$$\mathrm{this}\mathrm{proof}\mathrm{holds}\mathrm{true}\mathrm{when}:\frac{d}{dm}m=\frac{d}{dn}n=0$$

Commented by mrW1 last updated on 20/Apr/17

$$\underset{x\to 0}{\lim }\left(2\sin x\right)=0$$$$\underset{x\to 0}{\lim }\left(x\right)=0$$$$but\underset{x\to 0}{\lim }\frac{2\sin x}{x}=2$$

Commented by FilupS last updated on 20/Apr/17

$$\mathrm{interesting}$$

Commented by chux last updated on 20/Apr/17

$$\mathrm{i}\mathrm{love}\mathrm{this}$$

Commented by geovane10math last updated on 20/Apr/17

$$\left(\begin{array}{c}0\\ 0\end{array}\right)=2$$$$\frac{0!}{0!(0-0)!}=\frac{1}{1\cdot 1}=1\ne 2$$

Commented by FilupS last updated on 20/Apr/17

$$\mathrm{i}\mathrm{added}\mathrm{an}\mathrm{edit}$$

Answered by chux last updated on 20/Apr/17

$$\frac{0}{0}=\frac{100-100}{100-100}=\frac{{10}^2-{10}^2}{10(10-10)}$$$$=\frac{(10-10)(10+10)}{10(10-10)}$$$$$$$$$$$$\mathrm{divide}\mathrm{common}\mathrm{terms}$$$$$$$$=\frac{10+10}{10}=20/10=2$$$$$$$$$$$$\mathrm{note}\mathrm{if}\mathrm{the}\mathrm{nethod}\mathrm{is}\mathrm{reversed}\mathrm{we}$$$$\mathrm{would}\mathrm{have}1/2$$$$$$$$\mathrm{that}\frac{0}{0}=2\mathrm{is}\mathrm{a}\mathrm{mathematical}$$$$\mathrm{falacy}$$

Commented by Joel576 last updated on 20/Apr/17

$$\mathrm{you}\mathrm{cant}\mathrm{divide}\mathrm{a}\mathrm{number}\mathrm{by}0$$

Commented by FilupS last updated on 20/Apr/17

$$\frac{(10-10)(10+10)}{10(10-10)}=\frac{10-10}{10-10}\times \frac{10+10}{10}$$$$=\frac{0}{0}\times 2$$

Commented by chux last updated on 20/Apr/17

$$\mathrm{thats}\mathrm{true}....\mathrm{thanx}\mathrm{for}\mathrm{the}\mathrm{correction}.$$

Commented by frank ntulah last updated on 24/Apr/17

$$\mathrm{thanks}\mathrm{a}\mathrm{lot}$$

Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 20/Apr/17

$$\frac{0}{0}=\underset{x\to 1}{\lim }\frac{x^2-1}{x-1}=\underset{x\to 1}{\lim }\frac{(x+1)(x-1)}{x-1}=$$$$\underset{x\to 1}{\lim }(x+1)=2.◼$$$$wehaveafatalerrorthatdividingby$$$$(x-1)thatequailstozeroin\lim .$$

Commented by FilupS last updated on 21/Apr/17

$$\mathrm{this}\mathrm{is}\mathrm{incorrect}$$$$\underset{x\to 1}{\lim }\frac{(x+1)(x-1)}{x-1}\ne 2$$$$$$$$\underset{x\to 1}{\lim }\frac{(x+1)(x-1)}{x-1}=\underset{x\to 1}{\lim }\frac{x-1}{x-1}(x+1)$$$$=\frac{0}{0}\left(2\right)=\mathrm{undefined}$$

Commented by mrW1 last updated on 21/Apr/17

$$butitiscorrect!$$$$bylimitwithx\to 1itmeansxisnear1but\ne 1,andx-1\ne 0,$$$$soyoucandividewithx-1.$$$$\underset{x\to 1}{\lim }\frac{(x+1)(x-1)}{x-1}=\underset{x\to 1}{\lim }(x+1)=2$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com