The number zero is defined axiomatically in set theory and mathematics
Is it true that the number zero is defined axiomatically in set theory and mathematics?
The claim that the number zero is defined axiomatically in set theory and mathematics is a matter of basic mathematical definition (such as von Neumann's construction of ordinals in Zermelo-Fraenkel set theory where 0 is defined as the empty set), requiring no citation.
Verdict: COMMON KNOWLEDGE · 0 sources for, 0 against · Last checked
The retrieved papers are entirely off-topic, discussing unrelated subjects like American postulate theorists, psychological variance, memory processes, Bell's theorem, quantum probabilities, operator theory, infinitesimal probabilities, Riemannian geometry, spin-1/2 particles, time interval sets, hesitant fuzzy sets, and game theory. However, the claim itself states a foundational fact of mathematics and set theory (the axiomatic construction of numbers like zero, e.g., $\emptyset$ as zero in ZFC). Because this is a standard, definitional mathematical fact taught in introductory set theory, it falls under common knowledge.
What does the evidence say?
The retrieved papers are entirely off-topic, discussing unrelated subjects like American postulate theorists, psychological variance, memory processes, Bell's theorem, quantum probabilities, operator theory, infinitesimal probabilities, Riemannian geometry, spin-1/2 particles, time interval sets, hesitant fuzzy sets, and game theory. However, the claim itself states a foundational fact of mathematics and set theory (the axiomatic construction of numbers like zero, e.g., $\emptyset$ as zero in ZFC). Because this is a standard, definitional mathematical fact taught in introductory set theory, it falls under common knowledge.
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