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this.#data.set(key, new LWWRegister(this.id, register));
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If you relied on subtle semantics around the meaning of this in non-strict code, you may need to adjust your code as well.
This proof is known as Dirichlet’s approximation theorem. At first blush, it only guarantees a single 2-good approximation for every real. Worse yet, the solution guaranteed by the proof might not comply with the rules of our game, because nothing stops it from producing exact approximations (ε = 0). So, what did we achieve?