Does 1 have a degree of 1 or 0?

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Or is it both?
 

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  • #2
Office_Shredder
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Degree as what? A polynomial?
 
  • #3
arildno
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Does it matter?

For every real r, we have 1=1^r
 
  • #6
Office_Shredder
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It's a degree zero polynomial - if it was degree one it would have a variable term.
 
  • #7
arildno
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a*z^0 is a zero'th degree monomial in z, a first degree monomial in "a".
 
  • #8
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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?
 
  • #9
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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?
 
  • #10
arildno
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Do you understand the concept of a variable?
 
  • #11
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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 -∞, !?
 
  • #12
statdad
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"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''?
 
  • #13
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"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.
 
  • #14
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"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.
 
  • #15
HallsofIvy
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The degree of a polynomial, in variable x, is the highest power of x. We can write "1" as "[itex]1x^0[/itex]" so "degree 0". The reason for the distinction between the '0' polynomial (degree [itex]-\infty[/itex]) and the '1' (or any non-zero number) polynomial (degree 0) is that we could, theoretically, write 0 as "[itex]0x^n[/itex]" for any n.
 

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