1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

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

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    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

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

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

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    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

    User Avatar
    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''?
     
  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

    User Avatar
    Staff Emeritus
    Science Advisor

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Does 1 have a degree of 1 or 0?
  1. 0! = 1 (Replies: 24)

  2. Does 0^0 = 1 (Replies: 106)

  3. Why does e^(i*pi)+1=0? (Replies: 8)

Loading...