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#76 2013-08-12 08:09:04

bobbym
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Re: Change your subject.

Sometimes you might call t =0 today for instance. You could run the equation back to t=-3. That would be 3 days ago. The variable can take negative values.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#77 2013-11-14 20:53:01

EbenezerSon
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Re: Change your subject.

Is a member trying to indicate that a  number in a principal square root must have only one answer?
For instance, if 9 is in a principal square root, must it have only one answer 3?

If I am getting him wrong please correct.

Thanks.

How do you do Bobbym?

#78 2013-11-14 21:15:40

EbenezerSon
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Re: Change your subject.

The fellow's post is at #38.

What is the subtle difference between, a square root and a principal square root?

Thanks.

#79 2013-11-15 02:45:11

bobbym
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Re: Change your subject.

Hi;

The unique nonnegative square root of a nonnegative real number. For example, the principal square root of 9 is 3, although both -3 and 3 are square roots of 9.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#80 2013-11-15 19:40:07

EbenezerSon
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Re: Change your subject.

So if I am grasping it now, the principal square of a number produces only positive number.

Therefore, the principal square root  always infers a positive number.
Am I right?

Please confirm.

#81 2013-11-15 19:49:49

EbenezerSon
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Re: Change your subject.

Hi,

Please produce both the principal and the square root signs. So I will know thew properly

#82 2013-11-15 19:50:48

bobbym
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Re: Change your subject.

Therefore, the principal square root  always infers a positive number.

I would say yes.

http://www.mathsisfun.com/algebra/square-root.html


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#83 2013-11-15 20:33:04

EbenezerSon
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Re: Change your subject.

Hi,

I have browsed the link you provided, but couldn't distinguish the principal square root sign from the square root sign.

Some help.

#84 2013-11-15 20:39:03

anonimnystefy
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Re: Change your subject.

The square root sign

is usually used to indicate the principle square root of a number.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#85 2013-11-16 01:10:19

bobbym
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Re: Change your subject.

Hi;

Yep, that means positive root only.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#86 2013-11-16 01:38:34

EbenezerSon
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Re: Change your subject.

Okay, what name do we give to a negative square root of a number? Since the positive root number has a name.

Thanks in advance.

#87 2013-11-16 01:44:09

bobbym
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Re: Change your subject.

They are called complex or imaginary numbers.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#88 2013-11-16 01:55:59

EbenezerSon
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Re: Change your subject.

Okay, finally finally.
If I am getting
the whole thing, The square root of 9 is 3 and -3.
the 3 is the prıncipal square root whereas the negative square root -3 is complex or imaginary square root, am I correct?
Please confirm.

#89 2013-11-16 01:58:40

bobbym
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Re: Change your subject.

Both 3 and -3 when squared are 9. But only 3 is the principal square root.

√(-3) is complex or imaginary.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#90 2013-11-16 02:10:06

EbenezerSon
Full Member

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Re: Change your subject.

Please do you have an idea as to why it is called complex or imaginary?

#91 2013-11-16 02:14:25

bobbym
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Re: Change your subject.

It was called imaginary because in the beginning when the concept of the root of a negative number was proposed most mathematicians did not like it. They called them imaginary numbers to sort of poke fun at the whole idea. Later, as it caught on, complex numbers was name given for them.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#92 2013-11-16 02:52:23

EbenezerSon
Full Member

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Re: Change your subject.

Thanks for that!

But when 9 is in a square root sign it gives two answers i.e -3 and 3.
if the positive number is the principal square root what name is also given to the -3?

#93 2013-11-16 02:56:02

bobbym
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Re: Change your subject.

When 9 is in the square root sign that means principal square root, just the 3.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#94 2013-11-16 05:25:22

anonimnystefy
Real Member

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Re: Change your subject.

He is asking this:"If we call 3 the principal square root of 9, then what kind of square root of 9 is -3?". The answer is that there is no name given to it.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#95 2013-11-16 05:34:17

bobbym
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Re: Change your subject.

We could say it is the root of the equation x^2 - 9 = 0.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#96 2013-11-16 05:36:30

anonimnystefy
Real Member

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Re: Change your subject.

We could, but, there is still no special name for non-principal roots.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#97 2013-11-16 05:41:25

bobbym
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Re: Change your subject.

Everything you are saying is true but you are missing the point of my post #93 which essentially makes your post #94 non - essential.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#98 2013-11-16 05:55:46

anonimnystefy
Real Member

Offline

Re: Change your subject.

Actually, #94 is me feeling you have not understood the question.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#99 2013-11-16 05:57:57

bobbym
Administrator

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Re: Change your subject.

Nope, I was dealing with a far more important concept and did not answer that question. Do you see it now?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#100 2013-11-16 12:54:31

anonimnystefy
Real Member

Offline

Re: Change your subject.

But, what you said in #93 was already told and did not need repeating.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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