Very strange about the zero degree polynomial

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SUMMARY

The discussion centers on the properties of constant polynomials, specifically the expression f(x) = aX0, where a is a constant. It highlights the debate surrounding the value of 00, which is often considered indeterminate or undefined, yet is conventionally assigned the value of 1 in certain mathematical contexts. The participants clarify that while 00 may be undefined, polynomials are defined at x = 0, and thus the y-intercept exists without a hole on the y-axis. This distinction is crucial for understanding polynomial behavior and the implications of 00 in mathematical analysis.

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  • Understanding of polynomial functions and their properties
  • Familiarity with the concept of indeterminate forms in calculus
  • Knowledge of graphing functions and interpreting y-intercepts
  • Basic principles of power series and their definitions
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  • Research the implications of 00 in calculus and its treatment in various mathematical contexts
  • Study the properties of constant polynomials and their graphical representations
  • Explore the concept of indeterminate forms and how they affect limits and continuity
  • Learn about power series and their convergence criteria, particularly at boundary points
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Mathematicians, educators, and students studying polynomial functions, calculus, and mathematical analysis will benefit from this discussion.

Maisara-WD
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Hi everybody

f(x) = aX0 is the form of any constant polynomial... right??
eg: f(x) = 3 is actually f(x) =3X0 where X belongs to R... ok??

since 00 is an unspecified quantity.. therefore on graphing a constant.. it should exists a hole on y-axis... and the y-intercept should not satisfy the function ie: excluded from the solution set. am I right.. HELP
 
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00 was for a long time considered indeterminate or for some it was simply undefined. You have given one of a few reasons why 00 is conventionally given the value of 1 rather than 0 (there was much debate in the past over these two values specifically).
 
Even if 0^0 is considered undefined, polynomials are considered to be defined at 0. If you want to consider 0^0 undefined in general, then you will just have to get used to this convention. Also used for power series.
 

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