Does 1 have a degree of 1 or 0?

[student34]

Or is it both?

 

[Office_Shredder]

Degree as what? A polynomial?

 

[arildno]

Does it matter?

For every real r, we have 1=1^r

 

[student34]

Degree as what? A polynomial?

yes, as a polynomial

 

[student34]

Does it matter?

For every real r, we have 1=1^r

oh yeah

 

[Office_Shredder]

It's a degree zero polynomial - if it was degree one it would have a variable term.

 

[arildno]

a*z^0 is a zero'th degree monomial in z, a first degree monomial in "a".

 

[student34]

It's a degree zero polynomial - if it was degree one it would have a variable term.

Oh, so even though 5 has a power of 1, is it still considered a degree of 0?

 

[student34]

a*z^0 is a zero'th degree monomial in z, a first degree monomial in "a".

Ok, but what degree polynomial is 0 then?

 

[arildno]

Do you understand the concept of a variable?

 

[student34]

Do you understand the concept of a variable?

I have grade 12 algebra and grade 12 calculus, but any meaning of a variable beyond those courses, I am not sure.

I found an answer to the degree of 0; apparently it's -∞, !?

 

[statdad]

"I found an answer to the degree of 0; apparently it's -∞, !?"

No, you haven't. Constants are polynomials of degree 0.

What do you mean ``12 grade algebra and 12 grade calculus''?

 

[student34]

"I found an answer to the degree of 0; apparently it's -∞, !?"

No, you haven't. Constants are polynomials of degree 0.

I found it in my notes from my first year math course in university.

What do you mean ``12 grade algebra and 12 grade calculus''?

You have "12" and "grade" switched around.

 

[eigenperson]

"I found an answer to the degree of 0; apparently it's -∞, !?"

No, you haven't. Constants are polynomials of degree 0.

Some people do consider the degree of the zero polynomial to be -∞, so as to preserve rules like deg fg = deg f + deg g.

 

[HallsofIvy]

The degree of a polynomial, in variable x, is the highest power of x. We can write "1" as "$1x^0$" so "degree 0". The reason for the distinction between the '0' polynomial (degree $-\infty$) and the '1' (or any non-zero number) polynomial (degree 0) is that we could, theoretically, write 0 as "$0x^n$" for any n.