query: Definition of function application in ZF-like theories
positive_passages.docid: 16225
positive_passages.text: Set-theoretical definition of function evaluation
negative_passages.docid: 58267
negative_passages.text: Godel's pairing function and proving c = c*c for aleph cardinals
negative_passages.docid: 119982
negative_passages.text: how to express the set of natural numbers in ZFC
negative_passages.docid: 113182
negative_passages.text: Applying Zorn's lemma
negative_passages.docid: 54685
negative_passages.text: Defining metrics as a function to something other than the reals.
negative_passages.docid: 106284
negative_passages.text: Establishing a Basis for $F[x]/(f(x))$
negative_passages.docid: 84780
negative_passages.text: Cartesian products as sets of all functions.
negative_passages.docid: 83185
negative_passages.text: How to show countability of $\omega^\omega$ or $\epsilon_0$ in ZF?
negative_passages.docid: 142232
negative_passages.text: Functional Analysis. Continuous extensions of linear functionals.
negative_passages.docid: 73415
negative_passages.text: The reason why the existence of inaccessible cardinals cannot be proven in ZFC
negative_passages.docid: 20004
negative_passages.text: Meta Theory when studying Set Theory
negative_passages.docid: 53168
negative_passages.text: Surjective, Injective, Bijective Functions from $\mathbb Z$ to itself
negative_passages.docid: 56156
negative_passages.text: Composition and Onto Functions
negative_passages.docid: 15397
negative_passages.text: Is ZF2 based on MOVE?
negative_passages.docid: 102827
negative_passages.text: When do surjections split in ZF? Two surjections imply bijection?
negative_passages.docid: 43503
negative_passages.text: Bases of complex vector spaces and the axiom of choice
negative_passages.docid: 156536
negative_passages.text: Defining functions as derivatives