1. Boundary Configuration
LEM: APPLIED
NUMBER SYSTEM DOMAIN BOUNDARY ($\mathbb{D}$)
ℕ Naturals
ℤ Integers
ℚ Rationals
𝔸 Algebraic
ℝ Reals
System Telemetry & Metatheory
Existence Verdict:
proven_by_contradiction
Tertium Non Datur:
applied
Constructive Equivalent:
successive approximation
Foundation Limit:
relies on completed infinity
2. Logical Deduction Tree & Verification Canvas
D3 Render Engine Ready
Classical Analysis: In classical logic with tertium non datur, assuming $\neg P$ ($x \in \mathbb{Q}$ with $x^2 = 2$) derives $2b^2 = a^2 \implies a, b$ are both even, contradicting irreducible coprimality $\gcd(a,b)=1$. Classical logic negates the negation: $\neg \neg P \implies P$.
FORMAL DEDUCTION AUDIT TRAIL