## Prove me wrong

For students of class 11-12 (age 16+)
Dipan
Posts: 158
Joined: Wed Dec 08, 2010 5:36 pm

### Prove me wrong

0^0 = 0^{1 - 1} = 0^1.0^-1 = 0.0 = 0

I can't get what and where is the mistake ...can anyone help me??

nafistiham
Posts: 829
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### Re: Prove me wrong

$0^{-1}=\frac {1} {0}$
we can not divide anything by $0$
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.

Dipan
Posts: 158
Joined: Wed Dec 08, 2010 5:36 pm

### Re: Prove me wrong

I expected this answer...now see, if
$0^{-1}= \frac{1}{0}$
then,
$0 = 0^{1}=0^{2-1}=\frac{0^{2}}{0^{1}}=\frac{0}{0} so, \frac{0}{0}=0$
but 0/0 is undefined..... I am looking for another perfect answer....

tanvirab
Posts: 446
Joined: Tue Dec 07, 2010 2:08 am

### Re: Prove me wrong

negative powers of $0$ is undefined, as nafistiham already said.

Dipan
Posts: 158
Joined: Wed Dec 08, 2010 5:36 pm

### Re: Prove me wrong

make it clear to me.....which one is correct, $0^{-1}=\frac{1}{0}or, 0^{-1}=0$
$0^{-1}=\frac{1}{0}or, 0^{-1}=0$

*Mahi*
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### Re: Prove me wrong

Dipan wrote:make it clear to me.....which one is correct, $0^{-1}=\frac{1}{0}or, 0^{-1}=0$
$0^{-1}=\frac{1}{0}or, 0^{-1}=0$
Both are wrong.

Use $L^AT_EX$, It makes our work a lot easier!

Hasib
Posts: 238
Joined: Fri Dec 10, 2010 11:29 am
Location: খুলনা, বাংলাদেশ
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### Re: Prove me wrong

$0^{-1}$ is undefined. So, you can not write something equal to it.
A man is not finished when he's defeated, he's finished when he quits.

Dipan
Posts: 158
Joined: Wed Dec 08, 2010 5:36 pm

### Re: Prove me wrong

thanks Hasib and Mahi.....now this is clear to me......

nafistiham
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### Re: Prove me wrong

আমার মনে হয় $0 ^ {-1}$ যে কেন undefined তার একটা বিশদ আলোচনা প্রতি ক্লাসে একটু একটু করে থাকা উচিত । কারন, কেউ ভাগ শিখার সাথে সাথেই এই সমস্যার সম্মুখীন হয় । অথচ তাকে পুরোপুরি না বুঝিয়ে মুখস্ত করতে বলা হয় । তার পরও না বুঝার কারনে আমরা কত সমীকরণ ভুলভাবে তৈরি করি, আর ভুলটা বদ্ধমূল হতে থাকে ।
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.

MATHPRITOM
Posts: 190
Joined: Sat Apr 23, 2011 8:55 am
Location: Khulna

### Re: Prove me wrong

by courtesy of Zafar Iqbal sir.
for details see page 12,13,14,15 of his book "Goniter moja,mojar gonit."
look,now, we want to find the value of 1/0.
1/1=+1;
1/0.1=+10,
1/0.01=+100,
1/0.001=+1000,
so,we can say,when it is 1/0=+${\infty}$

but,1/-1=-1;
1/-0.1=-10,
1/-0.01=-100,
1/-0.001=-1000,
so,we can say,when it is 1/0=-${\infty}$;;
but,what is this......we got 2 different result of 1/0 ;one is +${\infty}$ & another is -${\infty}$;;so,1/0 is undefined.