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Packet G: Bonus 8

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> | Packet-G_Chicago-B_Ohio-State-A_UW-B

HeardPPBE %M %H %
5817.7697%36%45%

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Conversion

TeamOpponentPart 1Part 2Part 3TotalParts
DukeVirginia Tech A1001020EH
UNC BLiberty B10101030EMH
UNC CLiberty C100010E
UNC DWilliam & Mary100010E
Virginia ASouth Carolina100010E
Wake ForestLiberty A100010E

Summary

TournamentEditionMatchHeardPPBE %M %H %
California2025-02-01✓316.67100%33%33%
Florida2025-02-01✓313.3367%33%33%
Lower Mid-Atlantic2025-02-01✓615.00100%17%33%
Midwest2025-02-01✓618.33100%33%50%
North2025-02-01✓320.00100%33%67%
Northeast2025-02-01✓522.00100%60%60%
Overflow2025-02-01✓514.00100%20%20%
South Central2025-02-01✓220.00100%50%50%
Southeast2025-02-01✓412.5075%0%50%
UK2025-02-01✓1021.00100%70%40%
Upper Mid-Atlantic2025-02-01✓818.75100%25%63%
Upstate NY2025-02-01✓316.67100%33%33%