query: Can we make illegitimate operations with $0$ legitimate by adding a few more axioms?
positive_passages.docid: 22310
positive_passages.text: Why not to extend the set of natural numbers to make it closed under division by zero?
negative_passages.docid: 142840
negative_passages.text: Open axioms of equality
negative_passages.docid: 83842
negative_passages.text: Alternate proofs (other than diagonalization and topological nested sets) for uncountability of the reals?
negative_passages.docid: 78290
negative_passages.text: Countable axiom of choice: why you can't prove it from just ZF
negative_passages.docid: 3571
negative_passages.text: Equivalent implicit operators: why are they legal?
negative_passages.docid: 106799
negative_passages.text: Proof Verification: Converse of Intermediate Value Theorem
negative_passages.docid: 125263
negative_passages.text: How to crack the proof
negative_passages.docid: 9737
negative_passages.text: Complex number operations: telling Mathematica variables are real
negative_passages.docid: 139505
negative_passages.text: Peano/Presburger axioms - "find" numbers lower or equal than another number
negative_passages.docid: 27899
negative_passages.text: Can we prove the existence of $A\cup B$ without the union axiom?
negative_passages.docid: 2396
negative_passages.text: Order-preserving injections of ordinals into $[0,1]$
negative_passages.docid: 141496
negative_passages.text: Could someone make the proof into a hinted exercise?
negative_passages.docid: 95057
negative_passages.text: Possible fake proof of $1= -1$
negative_passages.docid: 116135
negative_passages.text: A paradox related to computable reals?
negative_passages.docid: 89535
negative_passages.text: fake proof of $\forall a. \forall b. a = b \to 1 = 0$
negative_passages.docid: 7865
negative_passages.text: Complete Newbie: Axiom of Foundation Exercise
negative_passages.docid: 56122
negative_passages.text: Is there any way to define pure functions with optional arguments?