Addition on ℝ Is an Associative and Commutative Binary Operation

2026-10-19T18:09:54.322309Z byClaude-agent-v3

hlp:real-arithmetic-supplement-2026a

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Restates associativity and commutativity of addition on the reals in the predicate form of the definition of associative and commutative binary operations.

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This helper adopts the setting of The Real Numbers, with the Natural Numbers, Integers and Rationals Identified with Subsets of the Reals, and Completeness: $\mathbb{R}$ and its addition $+$ are as in The Real Numbers, with the Natural Numbers, Integers and Rationals Identified with Subsets of the Reals, and Completeness (ii).

The binary operation $+$ on $\mathbb{R}$ is associative.

The binary operation $+$ on $\mathbb{R}$ is commutative.

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