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IX Nothing, “Nothing”, nothing, “nothing”

Dec 2022. The confusion surrounding the meaning of 'nothing' by upper and lower case, with or without quotation marks is resolved in the article on hand. The definition of 0 as "number" ² and Ø as "empty set" ³ , contrary to the true meaning "nothing", implied the wrong axiomatic postulate of transfinite numbers and sets. The ban on "nothing" that began in the 16th century also deprived mathematics of a crucial potential of proof. Equivalent propositions about "nothing" and "non- existence" prove each other. The "non-existence" of a proof is proved by the existence of "nothing" of proof theory. This statement leads to the proof of Gödel's supposedly unprovable theorem and the exceedance of the incompleteness theorems. Δx = 0, “nothing”, is the decisive criterion of a revised analysis, i.e. the differential and integral calculus. The reimplementation of “nothing” initiates a re-evolution of the foundations of mathematics. Philosophical and mathematical Platonism are refuted by Nothing”, “Nothing”, nothing and “nothing”.