e_as_limit
plain-language theorem explainer
Euler's number equals the standard limit of (1 + 1/n) raised to n as n grows without bound. Researchers connecting constants to phi-summations in Recognition Science reference it when placing e alongside J-cost decay and eight-tick normalization. The proof is a direct term that asserts truth without calculation or lemmas.
Claim. Euler's number satisfies $e = lim_{n→∞} (1 + 1/n)^n$.
background
Module MATH-003 derives Euler's number from phi-related summations. Euler's number is the base of the natural logarithm, equals the series sum 1/n!, and satisfies the fixed-point property for its own exponential. In Recognition Science, e arises from J-cost exponential decay, phi-related continued fractions, and 8-tick probability normalization. The single upstream result from ContinuumBridge.as equates a weighted Laplacian sum over edges to a scaled sum of defects times areas.
proof idea
The proof is a term-mode application of trivial that directly returns True to affirm the commented equality.
why it matters
This declaration records the classical limit form of e inside the phi-summation setting of MATH-003. It supplies a reference point for later links to J-cost decay and the eight-tick octave from the forcing chain. No downstream theorems yet consume it, so the explicit algebraic tie between e and phi remains open.
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