Math Is Fun Forum

21122012

Member

Registered: 2012-11-16

Posts: 278

Why in this 1=0?

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"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Why in this 1=0?

Where in the world did you get that?

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

21122012

Member

Registered: 2012-11-16

Posts: 278

Re: Why in this 1=0?

Where in the world did you get that?

What exactly? What letters or signs cause in you misunderstanding?

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"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Why in this 1=0?

Explain how you got the first equation...

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

21122012

Member

Registered: 2012-11-16

Posts: 278

Re: Why in this 1=0?

Explain how you got the first equation...

Look this:
h ttp://vladimir938.eto-ya.com/files/2012/12/screenshot-14.12.jpg
point 3.

Last edited by 21122012 (2012-12-15 07:36:08)

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"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

21122012

Member

Registered: 2012-11-16

Posts: 278

Re: Why in this 1=0?

seems to me that. And you as think?

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"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

Fistfiz

Member

Registered: 2012-07-20

Posts: 33

Re: Why in this 1=0?

seems like:

waaaaa

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30+2=28 (Mom's identity)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Why in this 1=0?

hi Fistfiz

If you accept the premise that 1 = 0, then you don't need calculus to get 2 = 1 (just add 1 to each side).

Alternatively suspect that 1 isn't 0 after all.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Fistfiz

Member

Registered: 2012-07-20

Posts: 33

Re: Why in this 1=0?

hi Fistfiz

If you accept the premise that 1 = 0, then you don't need calculus to get 2 = 1 (just add 1 to each side).

Alternatively suspect that 1 isn't 0 after all.

Bob

cool!

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30+2=28 (Mom's identity)

21122012

Member

Registered: 2012-11-16

Posts: 278

Re: Why in this 1=0?

seems like:

waaaaa

---

"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

Pshk

Guest

Re: Why in this 1=0?

I think  Mathematical analysis says that

.

round

Guest

Re: Why in this 1=0?

I think  Mathematical analysis says that

.

How can you divide by zero? May be you wanted to write:

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Why in this 1=0?

Hi round;

What does that mean??

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

21122012

Member

Registered: 2012-11-16

Posts: 278

Re: Why in this 1=0?

Here help:

:)

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"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Why in this 1=0?

Hi;

So 0 = 1? Gave me an idea!

Here is what I did. I had a 1 dollar bill in my pocket so I took it out and placed it in the drawer. But since I now had 0 dollars in my pocket immediately a dollar appeared in there. After all 0 dollars = 1 dollar. So I thought why not try this again. I took the dollar out and immediately it reappeared in my pocket! This worked again and again... Now the question is when should I stop?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

21122012

Member

Registered: 2012-11-16

Posts: 278

Re: Why in this 1=0?

It too difficult for me. I have not 1 dollar

Last edited by 21122012 (2012-12-16 13:30:18)

---

"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Why in this 1=0?

Here is what I did. I had a 1 dollar bill in my pocket so I took it out and placed in the drawer. But since I now had 0 dollars in my pocket immediately a dollar appeared in there. After all 0 dollars = 1 dollar. So I thought why not try this again. I took the dollar out and immediately it reappeared in my pocket! This worked again and again... Now the question is when should I stop?

  Stop when you have enough to live comfortably + 1 dollar.  Send that 1 dollar to me.  I have large pockets.

hhmmm.  I've seen this before.

Try

So

That looks OK to me.

Sorry bobbym   Your chance to become richer than Bill Gates has been dashed. 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Why in this 1=0?

Hi Bob

The problem with that is that the constand of integration appears after integration... In his steps, he never actually differentiated...

The flawed step is assuming that -Integral[1/x,x]+Integral[1/x,x]=0 instead of Integral [0,x].

Last edited by anonimnystefy (2012-12-16 22:14:28)

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Why in this 1=0?

hi Stefy,

You may be right.  My point is that this proof starts with a formula that I call 'integration by parts'.  This formula is obtained from the product rule, so differentiation is involved.

It is commonly assumed that integration is the reverse of differentiation.  I've even met teachers who teach this and books that state it.  It isn't true.

Differentation is a prescriptive process for working out a gradient function, say f(x), from a function, say F(x).

Integration is a summation process.  That's where the integral symbol comes from.  It is a stylised S.

http://en.wikipedia.org/wiki/Fundamenta … f_calculus

This makes clear that, if you have obtained F(x) by integration, then working out dF/dx gives f(x) once more.  But starting with F(x) and differentiating cannot be reversed to get F(x) back as there are infinitely many antiderivatives.

So whenever you use the antiderivative to obtain an integral, you must insert a constant of integration and failure to do so may well result in an answer that is wrong by a numeric amount.

I showed this at

http://www.mathisfunforum.com/viewtopic.php?id=18614

I consider the original statement to be correct, save for a numeric amount. 

In my opinion, that's why the proof appears to show an incorrect result, 1 = 0

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Fistfiz

Member

Registered: 2012-07-20

Posts: 33

Re: Why in this 1=0?

Hi Bob,

if I may, it seems to me that the (logical) error is deeper:
because

is just a symbol to denote the class of antiderivatives; so, saying class=number makes me think 21122012 is totally missing the meaning of it all.

---

30+2=28 (Mom's identity)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Why in this 1=0?

hi Fistfiz,

Have you looked at

http://www.mathisfunforum.com/viewtopic.php?id=18422

There's a lot of it, so I don't expect you to look at it all.  Post #1 is worth a look though.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Fistfiz

Member

Registered: 2012-07-20

Posts: 33

Re: Why in this 1=0?

I had a quick glance and it is very obscure to me; i'll try to read it later, thank you.

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30+2=28 (Mom's identity)

21122012

Member

Registered: 2012-11-16

Posts: 278

Re: Why in this 1=0?

So

That looks OK to me.

Sorry bobbym   Your chance to become richer than Bill Gates has been dashed. 

Bob

Give to me the website where this miracle except as here is still written?

This incorrect equality!

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"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

21122012

Member

Registered: 2012-11-16

Posts: 278

Re: Why in this 1=0?

Hi Bob

The problem with that is that the constand of integration appears after integration... In his steps, he never actually differentiated...

Last edited by 21122012 (2012-12-17 06:17:47)

---

"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!

21122012

Member

Registered: 2012-11-16

Posts: 278

Re: Why in this 1=0?

Hi Bob

The flawed step is assuming that -Integral[1/x,x]+Integral[1/x,x]=0 instead of Integral [0,x].

You are wrong. Such formula isn't present. Here a problem in other! Here a problem in an error of Calculus!

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"The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus"

Thomas Ioannes Stiltes. ...                                                 I made it!