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SMA_01
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Thank you for your help (and patience), I know it took a while for me to get it.
Proving algebraic numbers are countable?
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Homework Help Overview
The discussion revolves around proving that the set of algebraic numbers, specifically those obtained as roots of polynomials with integer coefficients of a given degree, is countable. The original poster presents a problem involving algebraic numbers defined by polynomials of degree n and seeks to understand how to utilize a provided hint regarding polynomial coefficients to support their proof.
Discussion Character
- Exploratory, Assumption checking, Problem interpretation
Approaches and Questions Raised
- Participants discuss the use of induction to prove the countability of algebraic numbers, with some questioning the applicability of the hint provided. Others suggest direct methods to show that the number of polynomials of a certain degree is countable, emphasizing the finite number of roots for each polynomial.
Discussion Status
The conversation reflects a mix of confusion and exploration of ideas, with participants attempting to clarify the implications of the hint and how to apply it effectively. Some participants have suggested that counting the number of integer polynomials under certain constraints could lead to a proof of countability, while others are still grappling with the initial steps of the argument.
Contextual Notes
Participants note the importance of establishing the countability of polynomials of degree n with integer coefficients and the implications of finite roots for these polynomials. There is an ongoing exploration of how to frame the proof without assuming conclusions prematurely.
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