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## #76 2013-08-12 08:09:04

bobbym

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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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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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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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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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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?

## #81 2013-11-15 19:49:49

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

## #87 2013-11-16 01:44:09

bobbym

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

## #89 2013-11-16 01:58:40

bobbym

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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
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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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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
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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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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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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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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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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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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

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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

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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.

anonimnystefy
Real Member

Offline