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#1 2014-06-12 10:53:16

MathsIsFun
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Registered: 2005-01-21
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Coefficient vs Constant

On the website I define a coefficient as "A number used to multiply a variable"

So, in

3 and 7 are coefficients and 2 is a constant. But is 2 also a coefficient?

How about in

Are a, b and c all coefficients?

(I want the simplest accurate definition.)


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#2 2014-06-12 10:59:47

Agnishom
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Re: Coefficient vs Constant

IMHO, it is. It is the coefficient of x^0

Go to sagecell.sagemath.org and run this code:

x = var('x')
expand((1+x)^6).coeff(x,n=0)

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#3 2014-06-12 11:30:11

Agnishom
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Re: Coefficient vs Constant

Wikipedia agrees too. http://en.wikipedia.org/wiki/Coefficient

Down the article, you have:

a45af437e8c5915d7f8751145e16877f.pngfor some integer , where  are coefficients; to allow this kind of expression in all cases one must allow introducing terms with 0 as coefficient.

Last edited by Agnishom (2014-06-12 11:30:43)


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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#4 2014-06-12 12:00:30

bobbym
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Re: Coefficient vs Constant

Hi;

It is a coefficient.


In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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#5 2014-06-12 12:30:58

MathsIsFun
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Re: Coefficient vs Constant

So, what is a good and easy to understand (for adults and children) definition of coefficient ... ?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#6 2014-06-12 12:40:01

bobbym
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Re: Coefficient vs Constant

Hi;

That is a good question. I do not know of a simple definition. Wiki takes 2 pages for it.


In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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#7 2014-06-12 12:45:07

David
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Re: Coefficient vs Constant

A constant used to multiply a variable


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#8 2014-06-12 12:47:13

bobbym
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Re: Coefficient vs Constant

Wikipedia uses:

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but in any case does not involve any variables of the expression.

The constant term is a coefficient as said already:

Enter this at Wolfram Alpha:

Coefficientlist of x^2 + 3x -8


In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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#9 2014-06-12 12:48:07

David
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Re: Coefficient vs Constant

o.o How is that easy to understand?


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#10 2014-06-12 12:50:26

Agnishom
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Re: Coefficient vs Constant

MathsIsFun wrote:

So, what is a good and easy to understand (for adults and children) definition of coefficient ... ?

A coefficient of a variable in some polynomial term is the constant by which it has been multiplied.

Last edited by Agnishom (2014-06-12 12:50:48)


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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#11 2014-06-12 12:51:08

bobbym
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Re: Coefficient vs Constant

That is what I am saying it is not easy. He will have to go into explaining that the -8 in x^2 + 3x -8 is a coefficient even though you do not see any variable connected to it.

Also, it does not have to be a polynomial:

The 2 and the -6 are coefficients.


In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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#12 2014-06-12 12:59:54

David
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Re: Coefficient vs Constant

This one is from google : 1.
MATHEMATICS
a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g., 4 in 4x y).


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#13 2014-06-12 13:13:27

MathsIsFun
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Re: Coefficient vs Constant

Yes, we normally draw a distinction between coefficient and constant, but then a constant is also a coefficient. A bit like a square is a rectangle.

How about

A number (or other fixed value) used to multiply in algebra.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#14 2014-06-12 13:14:32

David
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Re: Coefficient vs Constant

Multiply what in algebra?


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#15 2014-06-12 16:35:16

ganesh
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Re: Coefficient vs Constant

Hi MathsIsFun,

I learned in my school days, in the quadratic equation

a,b are coefficients; c is a constant  and x (and y, z) are variables.


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#16 2014-06-12 19:24:12

bob bundy
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Re: Coefficient vs Constant

hi MathsisFun,

Looking around the internet, there doesn't seem to be consistency about whether the constant term is a coefficient.  I suggest we say it is.  As to a formal definition, it is very hard to do this in a simple way.  Why bother?  If you give examples, then it becomes clear.  And if you say the coefficient c in ganesh's post is also often called the constant term, then you've covered it either way and alerted readers to the 'debate'.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#17 2014-06-12 19:48:27

MathsIsFun
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Posts: 7,560

Re: Coefficient vs Constant

Yes, it seems there is not consensus.

I do feel that having a constant also be a coefficient is more elegant (like a square being a rectangle).

How about

"The number (or other fixed value) part of a term."

With an example.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#18 2014-06-12 20:09:47

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 95,991

Re: Coefficient vs Constant

A good example will make it all clear.


In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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#19 2014-06-12 20:27:20

MathsIsFun
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Re: Coefficient vs Constant

OK, this is the new wording (so far), improvements welcome!

"The number (or other fixed value) part of a term, such as the 4 in 4y

A constant can also be though of as a coefficient. In ax² + bx + c, a, b and c are coefficients."


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#20 2014-06-12 20:46:28

bobbym
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From: Bumpkinland
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Posts: 95,991

Re: Coefficient vs Constant

Hi;

That is okay as far as it goes as long as you do not forget the t in thought. Post #11 shows one problem with that definition. Combinatorics and generating functions sort of make it easy to see that the constant term is a coefficient but a coefficient of what? In ax^2 + bx + c you say c is a coefficient of x^0 but in x + y + z +3 what is the 3 a coefficient of? x^0 or y^0 or (xy)^0. That might be difficult to explain.


In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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#21 2014-06-13 02:37:58

ShivamS
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Registered: 2011-02-07
Posts: 3,646

Re: Coefficient vs Constant

MathsIsFun wrote:

Are a, b and c all coefficients?

In my opinion (along with asking a few professors here for their opinions), a and b are coefficients of x^2 and x respectively and c of x^0. However, we can't say that c is a coefficient in ax^2 + bx + c, but we can say it is in ax^2 + bx + cx^0.

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#22 2014-06-13 03:07:42

anonimnystefy
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From: The Foundation
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Posts: 15,922

Re: Coefficient vs Constant

The way I understand it:

1) c is a coefficient in that polynomial;

2)coefficient is a constant used in a polynomial. I have not seen the term coefficient used much elsewhere.


“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
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#23 2014-06-13 03:08:40

ShivamS
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Re: Coefficient vs Constant

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#24 2014-06-13 09:56:51

MathsIsFun
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Re: Coefficient vs Constant

ShivamS wrote:

However, we can't say that c is a coefficient in ax^2 + bx + c, but we can say it is in ax^2 + bx + cx^0.

That makes sense.

What does everyone think about that?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#25 2014-06-13 11:02:23

anonimnystefy
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Registered: 2011-05-23
Posts: 15,922

Re: Coefficient vs Constant

I think it's a bit confusing considering the two are the same. And I'd rather call it a coefficient than not.


“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.

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