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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>

EditionsHeardPPBEasy %Medium %Hard %
15817.7697%36%45%

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Conversion

TeamOpponentPart 1Part 2Part 3TotalParts
BristolCambridge D10101030EMH
Cambridge ACambridge E10101030EMH
Cambridge BWarwick B10101030EMH
DurhamOxford B1010020EM
LSEOxford C1010020EM
ManchesterSouthampton B100010E
NYU CImperial A100010E
Oxford ASouthampton A10101030EMH
SheffieldImperial B100010E
Warwick ACambridge C1010020EM

Summary

TournamentEditionHeardPPBEasy %Medium %Hard %
California2025-02-01316.67100%33%33%
Florida2025-02-01313.3367%33%33%
Lower Mid-Atlantic2025-02-01615.00100%17%33%
Midwest2025-02-01618.33100%33%50%
North2025-02-01320.00100%33%67%
Northeast2025-02-01522.00100%60%60%
Overflow2025-02-01514.00100%20%20%
South Central2025-02-01220.00100%50%50%
Southeast2025-02-01412.5075%0%50%
UK2025-02-011021.00100%70%40%
Upper Mid-Atlantic2025-02-01818.75100%25%63%
Upstate NY2025-02-01316.67100%33%33%