absolute value - 2025 ACF Winter

Question

Answer the following about functions that are continuous and not differentiable, for 10 points each.

[10e] This non-negative function is continuous everywhere but is not differentiable at zero. A vertical bar on each side of the input is used to symbolize this function.

ANSWER: absolute value [or modulus; or magnitude; or L1-norm; prompt on norm]

[10h] The existence of a function that is continuous but nowhere differentiable can be proved by showing that the set of anywhere differentiable functions is meager in the space of continuous functions, then applying this person’s namesake “category theorem.”

ANSWER: René-Louis Baire (“bair”) [accept Baire category theorem]

[10m] The vertical bar notation for absolute value was introduced by this person, who names a continuous but nowhere differentiable function equal to a sum of cosines of exponentially-growing frequency. Bernard Bolzano and this person co-name a theorem showing that convergent subsequences exist for bounded sequences.

ANSWER: Karl Weierstrass [or Karl Theodor Wilhelm Weierstrass; accept Weierstrass function; accept Bolzano–Weierstrass theorem]

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Summary


California	Main	Y	5	20.00	100%	80%	20%
Canada	Main	Y	5	22.00	100%	100%	20%
Florida	Main	Y	12	15.83	100%	50%	8%
Great Lakes	Main	Y	6	10.00	83%	17%	0%
Lower Mid-Atlantic	Main	Y	7	14.29	86%	57%	0%
Midwest	Main	Y	8	11.25	75%	38%	0%
North	Main	Y	10	14.00	100%	30%	10%
Northeast	Main	Y	5	20.00	100%	80%	20%
Overflow	Main	Y	4	15.00	100%	50%	0%
Pacific Northwest	Main	Y	10	17.00	90%	60%	20%
South Central	Main	Y	5	12.00	100%	20%	0%
Southeast	Main	Y	1	20.00	100%	100%	0%
UK	Main	Y	4	17.50	75%	100%	0%
Upper Mid-Atlantic	Main	Y	8	17.50	88%	50%	38%
Upstate NY	Main	Y	8	13.75	88%	25%	25%
2025 ACF Nationals	2025-08-09	Y	3	20.00	100%	100%	0%
2024 ARCADIA at UC Berkeley	04/19/2025	Y	4	20.00	100%	75%	25%

Data


Berkeley D	Berkeley B	10	0	10	20
Stanford A	Berkeley C	10	10	10	30
Berkeley E	UCSC	10	0	0	10
Stanford B	Berkeley F	10	0	10	20
Berkeley A	Stanford C	10	0	10	20
Claremont Scripps	USC	10	0	10	20
UCLA B	UCLA C	10	10	10	30
UCI	UCSB	10	0	10	20
UCSD Two Running Violet V Forms	Claremont Pitzer	10	0	10	20
UCSD Vices and Virtues	UCSD What Hath God Wrought	10	0	10	20
Guelph B	Queen's A	10	0	0	10
Ottawa	Guelph A	10	0	0	10
Queen's B	Toronto G	10	0	0	10
Toronto A	McGill A	10	0	10	20
Toronto D	Toronto C	10	0	10	20
Toronto I	Toronto F	10	0	0	10
Toronto H	McGill B	10	10	10	30
Toronto J	Toronto E	10	0	10	20
Toronto K	Western Ontario	10	0	0	10
Toronto B	Toronto Metropolitan	10	0	10	20
McMaster C	Waterloo	10	0	10	20
McMaster A	McMaster B	10	0	0	10
ERAU A	UF A	0	0	0	0
UCF B	UF C	10	0	0	10
UF B	UCF A	10	0	10	20
ERAU B	UF E	10	0	0	10
Melbourne B	FSU	10	0	0	10
CWRU A	Kenyon A	10	0	10	20
OSU B	CWRU D	10	0	0	10
Pitt A	Kenyon B	10	0	10	20
OSU A	MSU A	10	0	10	20
Pitt C	OSU C	0	0	0	0
MSU B	OSU D	10	0	10	20
Pitt B	CWRU C	10	0	0	10
Melbourne A	USF	10	0	0	10
Clemson A	North Carolina C	10	0	0	10
South Carolina A	Clemson B	0	0	10	10
North Carolina A	Tennessee A	0	0	10	10
North Carolina B	Roanoke	10	0	0	10
Liberty C	Tennessee B	10	0	0	10
Tusculum	Liberty B	10	0	10	20
Virginia Tech B	Virginia A	10	0	0	10
Virginia Tech A	Virginia B	10	0	0	10
George Mason B	Johns Hopkins C	10	0	0	10
Maryland B	George Washington B	10	0	0	10
Johns Hopkins B	Catholic University	10	0	0	10
George Mason A	Maryland A	10	0	0	10
Maryland C	Notre Dame E	10	0	10	20
NYU A	Maryland D	10	10	10	30
Georgetown B	NYU B	10	0	0	10
Georgetown A	UMBC A	10	0	0	10
VCU A	Penn B	10	0	10	20
George Mason C	Penn A	10	0	0	10
Columbia A	Rutgers B	10	10	10	30
Princeton A	Vassar A	10	0	10	20
Rutgers C	Columbia C	10	0	10	20
Swarthmore A	Rowan A	10	0	10	20
Missouri A	Truman State	10	0	10	20
SIUE	WashU A	10	0	10	20
WashU D	WashU B	10	0	0	10
William Woods	Missouri B	10	0	0	10
Lehigh A	Lehigh B	10	0	0	10
Chicago A	Illinois B	10	10	10	30
Indiana A	Chicago B	10	10	10	30
Illinois A	Notre Dame C	10	0	10	20
Notre Dame A	Illinois C	10	0	10	20
Indiana B	Chicago C	0	0	0	0
Michigan A	Louisville A	10	0	10	20
Michigan C	Notre Dame B	10	0	0	10
Purdue A	Michigan D	10	0	10	20
Purdue B	Chicago D	10	0	0	10
Purdue C	UIC	10	0	0	10
Nebraska	Macalester B	10	0	0	10
St. Thomas	Minnesota A	10	0	0	10
Minnesota B	Iowa State	10	0	0	10
Macalester A	Minnesota C	10	0	0	10
Carleton	Wisconsin	10	0	10	20
Yale B	Bowdoin A	10	0	10	20
Washington A	Washington B	10	0	10	20
Alberta	Simon Fraser	0	0	10	10
British Columbia A	British Columbia B	10	0	10	20
British Columbia D	British Columbia C	10	0	10	20
Tulsa	Alberta B	10	0	0	10
McGill D	Arizona State B	0	10	10	20
Ohio	Northwestern C	10	0	0	10
Rose State	UTD B	10	0	0	10
Texas A	Iowa	10	0	10	20
Northwestern B	Texas B	10	10	10	30
UCO	Northwestern A	10	0	0	10
Arizona State A	UTD A	10	10	10	30
Auburn A	Sewanee A	10	10	10	30
Georgia Tech A	Bruin A	0	10	10	20
Georgia Tech C	Mississippi State A	10	0	0	10
Georgia Tech D	UAB A	10	0	0	10
Georgia Tech B	Huntsville A	10	0	0	10
Huntsville B	Auburn B	10	0	0	10
Vanderbilt A	Alabama B	10	0	0	10
Vanderbilt B	Alabama A	10	0	0	10
LSE B	Warwick B	10	0	10	20
Edinburgh B	Manchester B	10	0	10	20
Bristol A	Cambridge A	10	0	10	20
Cornell-DII	RIT A	10	0	10	20
RIT B	Binghamton A	10	10	10	30
Binghamton B	Rochester	10	0	10	20
Syracuse	ESF	10	0	0	10