Discussion Overview
The discussion centers around the meaning of the triangle equals sign (\triangleq) and its distinction from the triple equals sign (\equiv). Participants explore its usage in mathematical contexts, particularly in relation to definitions and identities.
Discussion Character
- Technical explanation, Conceptual clarification, Debate/contested
Main Points Raised
- Some participants note that \triangleq is encountered in mathematical literature, specifically mentioning its appearance in the context of the Lie derivative.
- It is proposed that \triangleq is used to signify "is defined as" or "equals by definition."
- One participant expresses agreement with the definition provided by another.
- A question is raised regarding the difference in meaning between \triangleq and the triple-equals sign (\equiv).
- Another participant suggests that the triple-equals sign is typically used to indicate that a function identically equals a constant or another function.
Areas of Agreement / Disagreement
Participants generally agree on the definition of \triangleq as a symbol for "is defined as," but there is a question regarding its distinction from \equiv, indicating that the discussion remains unresolved on this point.
Contextual Notes
The discussion does not clarify the precise mathematical contexts in which each symbol is used, nor does it address potential variations in definitions across different fields.