We publish our audit record because accuracy claims should be checkable. Every entry on this site runs through an automated fact-audit pipeline (accuracy audit → source-grounded repair → visual QA); this page is generated from that pipeline's own report, not written by hand.
Last full accuracy audit: 2026-09-05 · 20 entries checked · 5 flagged · 8 issues confirmed · 0 corrected · 8 still open
Axiom of extensionality — The entry states that in Quine's 1937 paper, equality was defined as ∀z (x ∈ z → y ∈ z), but Quine's 1937 paper actually defined equality as ∀z (z ∈ x ↔ z ∈ y).
Axiom of extensionality — The 'DID YOU KNOW' section claims that in Quine's New Foundations (1937), the principle of extensionality was given as the postulate P1: x ⊂ y → (y ⊂ x → x = y), but Quine's 1937 paper actually gives the extensionality postulate as ∀x∀y (∀z (z ∈ x ↔ z ∈ y) → ∀
Axiom of pairing — The claim that the axiom of pairing 'follows from the axiom schema of replacement applied to any given set with two or more elements' is imprecise; the standard derivation uses replacement on a two-element set and requires the existence of at least one set (e.
Axiom of pairing — The statement 'The existence of a set with two elements, such as { {}, { {} } }, can be deduced either from the axiom of empty set and the axiom of power set or from the axiom of infinity' is factually incorrect; the empty set and power set alone do not suffic
Axiom schema of specification — The claim that the axiom schema of specification was introduced in 1930 by Thoralf Skolem is incorrect; Skolem introduced it in 1922.
Axiomatic system — The claim that 'Georg Cantor's abstract set theory' was developed in the nineteenth century as a major axiomatic system is misleading; Cantor's set theory was not axiomatized until the early twentieth century.
Cantor set — The Cantor set was not discovered by Henry John Stephen Smith in 1874; Smith published a construction of a set with similar properties in 1875, but the set now known as the Cantor set was introduced by Georg Cantor in 1883.
Cantor set — The statement that Cantor mentioned the ternary construction only in passing is misleading; Cantor explicitly described the ternary construction in his 1883 paper as a key example of a perfect set that is nowhere dense, not merely in passing.
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