Question
Answer the following about the construction of the p-adic numbers, for 10 points each.
[10e] The p-adic numbers can be formally defined as one of these constructs expressed using a rational times all powers of p. Taylor and Maclaurin name examples of these expansions used to represent smooth functions.
ANSWER: power series [accept formal series; prompt on infinite summation]
[10m] Under the p-adic norm, the p-adics are a completion of the rationals, meaning that each of these sequences converges to a limit in the set. In one of these sequences, all terms past a certain point become arbitrarily close.
ANSWER: Cauchy (“KO-shee”) sequences
[10h] To obtain other completions in the field of fractions, one can localize a type of integral domain named for this mathematician. A construction named for this mathematician partitions the rationals into “left” and “right” sets.
ANSWER: Richard Dedekind [accept Dedekind domain or Dedekind cut]
<AR, Other Science>
Summary
| California | 2025-02-01 | Y | 3 | 16.67 | 100% | 33% | 33% |
| Florida | 2025-02-01 | Y | 3 | 13.33 | 67% | 33% | 33% |
| Lower Mid-Atlantic | 2025-02-01 | Y | 6 | 15.00 | 100% | 17% | 33% |
| Midwest | 2025-02-01 | Y | 6 | 18.33 | 100% | 33% | 50% |
| North | 2025-02-01 | Y | 3 | 20.00 | 100% | 33% | 67% |
| Northeast | 2025-02-01 | Y | 5 | 22.00 | 100% | 60% | 60% |
| Overflow | 2025-02-01 | Y | 5 | 14.00 | 100% | 20% | 20% |
| South Central | 2025-02-01 | Y | 2 | 20.00 | 100% | 50% | 50% |
| Southeast | 2025-02-01 | Y | 4 | 12.50 | 75% | 0% | 50% |
| UK | 2025-02-01 | Y | 10 | 21.00 | 100% | 70% | 40% |
| Upper Mid-Atlantic | 2025-02-01 | Y | 8 | 18.75 | 100% | 25% | 63% |
| Upstate NY | 2025-02-01 | Y | 3 | 16.67 | 100% | 33% | 33% |