Natural Number Addition is Closed
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- $\forall x, y \in \N: x + y \in \N$
Follows directly from Natural Numbers under Addition form Commutative Monoid.
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 5.1$. Subsets closed to an operation: Example $88$
- 1971: Gaisi Takeuti and Wilson M. Zaring: Introduction to Axiomatic Set Theory: $\S 8.9$
- 1974: Murray R. Spiegel: Theory and Problems of Advanced Calculus (SI ed.) ... (previous) ... (next): Chapter $1$: Numbers: Real Numbers: $1$
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): Chapter $1$: Complex Numbers: The Real Number System: $1$