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Does 1 have a degree of 1 or 0?

  1. Sep 28, 2013 #1
    Or is it both?
     
  2. jcsd
  3. Sep 28, 2013 #2

    Office_Shredder

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    Degree as what? A polynomial?
     
  4. Sep 28, 2013 #3

    arildno

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    Does it matter?

    For every real r, we have 1=1^r
     
  5. Sep 28, 2013 #4
    yes, as a polynomial
     
  6. Sep 28, 2013 #5
    oh yeah
     
  7. Sep 28, 2013 #6

    Office_Shredder

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    It's a degree zero polynomial - if it was degree one it would have a variable term.
     
  8. Sep 28, 2013 #7

    arildno

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    a*z^0 is a zero'th degree monomial in z, a first degree monomial in "a".
     
  9. Sep 28, 2013 #8
    Oh, so even though 5 has a power of 1, is it still considered a degree of 0?
     
  10. Sep 28, 2013 #9
    Ok, but what degree polynomial is 0 then?
     
  11. Sep 28, 2013 #10

    arildno

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    Do you understand the concept of a variable?
     
  12. Sep 28, 2013 #11
    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 -∞, !?
     
  13. Sep 28, 2013 #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''?
     
  14. Sep 28, 2013 #13
    I found it in my notes from my first year math course in university.

    You have "12" and "grade" switched around.
     
  15. Sep 28, 2013 #14
    Some people do consider the degree of the zero polynomial to be -∞, so as to preserve rules like deg fg = deg f + deg g.
     
  16. Oct 3, 2013 #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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