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...his friend's credit card number. Much like {{w|The Library of Babel}}, an axiom system which can prove ''any'' statement might as well prove nothing. Perha

...position and time of any particle in the system can be described. It is an axiom of Newtonian Mechanics that there exist "Inertial Frames." In an inertial f

| titletext = Proof of Zermelo's well-ordering theorem given the Axiom of Choice: 1: Take S to be any set. 2: When I reach step three, if S hasn't The {{w|axiom of choice}} (which has been referenced previously in [[804: Pumpkin Carving

...g Cueball's unexpected result would not have happened without using the axiom. ...et theory was later referenced in [[982: Set Theory]] and, much later, the axiom of choice was mentioned again in the title text of [[1724: Proofs]].

...upon Megan's motivations and self-awareness, as she could be breaking the axiom intentionally (giving the statement a grander preface than she fully knows

| titletext = Next, let's assume the decision of whether to take the Axiom of Choice is made by a deterministic process ... ...}, where many statements become impossible to prove or disprove if the {{w|axiom of choice}} is not taken as a part of the axiomatic system.

...{{w|beth zero}} and {{w|beth one}} (and analogously for {{w|Large cardinal axiom#Hierarchy of consistency strength|large cardinal axioms}}, so mathematician

....S.S.}}''), and just a day after the latest flight to the station by a {{w|Axiom Mission 3|Crew Dragon flight}} had temporarily increased the occupants from

...een ''proven'' from former accepted statements, like other theorems or {{w|axiom}}s. This comic references {{w|Rolle's theorem}}. The theorem essentially st

...which is equivalent (given {{w|Zermelo–Fraenkel set theory}}) to the {{w|axiom of choice}}, the subject of [[982: Set Theory]]. This principle would apply

...completeness theorems}}. In it a unique natural number is assigned to each axiom, statement, and proof, which might otherwise be difficult to accurately pro ...ure to Gödel's particular statement" is not precise enough to serve as an axiom.). As such, with a little more legwork, it can be proven that any logical