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LordCalculus
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Find the p-adic volume of the p-adic circle x^2 + y^2 = 1.
This isn't hw.
This isn't hw.
What Is the P-adic Volume of the P-adic Circle x² + y² = 1?
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Discussion Overview
The discussion revolves around the concept of the p-adic volume of the p-adic circle defined by the equation x² + y² = 1. Participants explore the mathematical implications and requirements for determining this volume, including the necessary tools and concepts from p-adic analysis.
Discussion Character
- Exploratory, Technical explanation, Conceptual clarification
Main Points Raised
- One participant suggests that the concept of p-adic pi may be relevant to finding the p-adic volume.
- Another participant proposes that measure and integration are necessary tools for this calculation and references Koblitz's work on p-adic numbers and zeta-functions.
- There is uncertainty expressed regarding whether the curve encloses a finite area, with one participant explicitly questioning this aspect.
- A participant mentions a lack of familiarity with p-adic numbers, indicating that the context of the question is not well-defined in the materials provided.
Areas of Agreement / Disagreement
Participants express uncertainty about the nature of the area enclosed by the curve and the necessary mathematical framework to approach the problem. There is no consensus on whether the area is finite or the specific methods to be used.
Contextual Notes
Limitations include a lack of clarity on the definitions of p-adic numbers and the assumptions required for measuring the area of the curve. The discussion does not resolve whether the curve encloses a finite area.
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