41. In the absence of the axiom of choice , total boundedness and precompactness must be distinguished. 42. Without the axiom of choice , these theorems may not hold for mathematical objects of large cardinality. 43. Not every situation requires the axiom of choice . 44. This paper led to the general acceptance of the axiom of choice in the mathematics community. 45. Skepticism about the axiom of choice was reinforced by recently discovered paradoxes in naive set theory. 46. The axiom of choice , of course, is true. 47. This result depends on the axiom of choice . 48. All of the above proofs use the axiom of choice ( AC ) in some way. 49. This version of complete distributivity only implies the original notion when admitting the Axiom of Choice . 50. The former result opened the door for mathematicians to assume the axiom of choice in their proofs.
