ZERO AND INFINITY / FORMAL BOUNDARY
The O/0 documents use zero and infinity as boundary symbols: one suggests no quantity; the other suggests unbounded quantity. Their shared ability to strain ordinary intuition is spiritually and philosophically productive.
In standard arithmetic, division by zero is undefined. Infinity is not an ordinary real number, and rotating the glyph 0 does not establish an algebraic identity with infinity.
The empty set can serve as a foundation in standard set-theoretic constructions of numbers, but that formal role does not establish that physical existence emerged from metaphysical nothingness.
Archive judgment: retain 0 ↔ ∞ as symbolic notation and formal conjecture. Do not label 0 = ∞ a proved mathematical theorem without a precisely defined nonstandard system.
External anchor: NIST Digital Library of Mathematical Functions, notation and extended complex-plane conventions — https://dlmf.nist.gov/not/