Discussion Overview
The discussion revolves around the search for a symbol representing the concept of "probably equals" in mathematical notation. Participants explore various interpretations of "probably" and its implications in different contexts, including probability and statistics, as well as philosophical considerations regarding definitions and subsets.
Discussion Character
- Exploratory
- Debate/contested
- Conceptual clarification
Main Points Raised
- Some participants note existing symbols for related concepts, such as approximately equals and almost surely, but express that there is no widely accepted symbol for "probably equals."
- One participant suggests using the symbol ≟ or the notation a.s. (almost surely) as alternatives, while others caution that these may not accurately convey the intended meaning.
- There is a discussion about the ambiguity of the term "probably," with some suggesting that its meaning can vary based on context, such as whether it refers to a probability or a qualitative assessment.
- Another participant proposes using subset notation to express relationships, such as "cat is a subset of animal," while emphasizing the need for careful interpretation of equalities.
- Some participants argue that if "probably" is not quantifiable, it may not have a corresponding mathematical symbol, while others suggest that context-sensitive symbols could be adapted for this purpose.
- There is mention of using a percentage over the equals sign to indicate a degree of likelihood, though no specific symbol is identified.
- One participant introduces the idea of "truthlikeness" in non-binary logic as a way to express degrees of truth, suggesting that this could relate to the concept of "probably equals."
- A later reply highlights the challenge of defining a new category for "probably equals" within existing mathematical frameworks, suggesting that it may require further development.
Areas of Agreement / Disagreement
Participants generally agree that there is no established symbol for "probably equals," but there are multiple competing views on how to express the concept, and the discussion remains unresolved regarding a definitive notation.
Contextual Notes
Participants acknowledge that the meaning of "probably" can vary significantly depending on context, and there are unresolved questions about how to appropriately represent this concept mathematically.