# Does 1 have a degree of 1 or 0?

Or is it both?

Office_Shredder
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Degree as what? A polynomial?

arildno
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Does it matter?

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

Degree as what? A polynomial?

yes, as a polynomial

Does it matter?

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

oh yeah

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

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

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?

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
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Do you understand the concept of a variable?

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 -∞, !?

Homework Helper
"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''?

"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.

"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.