| 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.
|
