The Tonawanda Kardex (also known as the Tonawanda Lumbermen and during its first season, the All-Tonawanda Lumberjacks ) was an American football team active between 1916 and 1921. It played its games in Tonawanda, New York , a suburb of Buffalo with close ties to North Tonawanda, New York where American Kardex was founded. The team is most notable for its one game as a member of the American Professional Football Association (now the National Football League ) in the 1921 season. They are easily the shortest-lived team in the league's history, and the shortest-lived known team in North American major league sports history.
20-653: Professional football was being played in Tonawanda by no later than 1913 (this terminus ad quem comes from records that show the team lost to the Lancaster Malleables in the region's showcase Thanksgiving game that year). They played their home games on the Tonawanda High School field, sometimes drawing up to 3,500 fans for a game. For the team's entire history, it was coached by Syracuse standout Walter "Tam" Rose . In 1917, it defeated
40-431: A terminus ad quem 'limit to which' is the latest possible date of a non-punctual event (period, era, etc.), whereas a terminus a quo 'limit from which' is the earliest. The concepts are similar to those of upper and lower bounds in mathematics. These terms are often used in archaeological and historical studies, such as dating layers in excavated sites, coins, historical events, authors, inscriptions or texts where
60-495: A subset S of some preordered set ( K , ≤) is an element of K that is greater than or equal to every element of S . Dually , a lower bound or minorant of S is defined to be an element of K that is less than or equal to every element of S . A set with an upper (respectively, lower) bound is said to be bounded from above or majorized (respectively bounded from below or minorized ) by that bound. The terms bounded above ( bounded below ) are also used in
80-475: A terminus are known dates of death or travel by persons involved, a particular form of heraldry that can be dated (see pastiglia for example), references to reigning monarchs or office-holders, or a placing relative to any other events whose date is securely known. In a modern context, dated images, such as those available in Google Earth , may establish termini. A terminus ante quem non differs from
100-436: A terminus ante quem would be deposits formed before a historically dateable event, such as building foundations that were partly demolished to make way for the construction of a city wall. If it is known that the wall was finished in 650, then the foundations must have been demolished in 650 or earlier; all that can be said from the evidence is that it happened before the known event. Other examples of things that may establish
120-454: A terminus post quem by not implying the event necessarily took place. 'Event E happened after time T' implies E occurred, whereas 'event E did not happen before time T' leaves open the possibility that E never occurred at all. In project planning , sometimes the phrases "no earlier than" / "no later than" (NET/NLT) are used. Upper and lower bounds In mathematics , particularly in order theory , an upper bound or majorant of
140-672: A 35–0 decision to Buffalo). Their last game of the season against the Rochester Jeffersons was among the first games in the traditional Thanksgiving Day series . With their 1920 success (and a crackdown by the APFA on playing non-league teams), the Lumberjacks joined the league in 1921 as the Tonawanda Lumbermen or Tonawanda Kardex, named for (and presumably sponsored by) James Rand Jr. 's American Kardex,
160-453: A company that through mergers and acquisitions became part of Rand Kardex, Remington Rand , Sperry Rand , and eventually UniSys . Before 1921, the team played its home games at Tonawanda High School; however, its lone game in the NFL was an away game, and according to contemporary news reports, the team had intended to play as a traveling team had it continued beyond one game. NFL records list
180-421: A lower bound; all other numbers are either an upper bound or a lower bound for that S . Every subset of the natural numbers has a lower bound since the natural numbers have a least element (0 or 1, depending on convention). An infinite subset of the natural numbers cannot be bounded from above. An infinite subset of the integers may be bounded from below or bounded from above, but not both. An infinite subset of
200-489: A second season in the league. The team's declining on-field performance was also a factor (Rochester and Syracuse were two teams that Tonawanda had beaten handily as an independent in 1920 but performed far less well against as a league member in 1921). Whether or not the team continued to exist is somewhat unclear. Records from 1925 show that the Buffalo Football Bisons played an exhibition game against
220-436: A set of functions, if it is an upper bound of each function in that set. The notion of lower bound for (sets of) functions is defined analogously, by replacing ≥ with ≤. An upper bound is said to be a tight upper bound , a least upper bound , or a supremum , if no smaller value is an upper bound. Similarly, a lower bound is said to be a tight lower bound , a greatest lower bound , or an infimum , if no greater value
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#1732772757677240-999: A team from Tonawanda before the 1925 regular season , but it is not known if it is the same Tonawanda team as the APFA/NYPFL franchise. The "Lumberjacks" name is currently in use by North Tonawanda High School . Due to incomplete record-keeping during this time, some players from the 1921 team are only reported upon by their last name. Backnor, C; Fred Brumm, LT; Cassidy, QB; Joe Dussosoit, RE; Andy Fletcher, LHB; Art Georke, LE; Clarence Hosmer, LG; Rudy Kraft, LG-C; George Kuhrt, LT; Buck MacDonald, RG; Tom McLaughlin, RHB-FB; Bill Meisner, RHB; Frank Morrisey, RT; Frank Primeau, RE-QB; Tam Rose, LHB; Spin Roy, LE; Bill Sanborn, RE; Charles Tallman, RT; Red Werder, C; Wex, FB;Wise, QB Terminus post quem A terminus post quem ('limit after which', sometimes abbreviated TPQ ) and terminus ante quem ('limit before which', abbreviated TAQ ) specify
260-407: Is called sharp if equality holds for at least one value of x . It indicates that the constraint is optimal, and thus cannot be further reduced without invalidating the inequality. Similarly, a function g defined on domain D and having the same codomain ( K , ≤) is an upper bound of f , if g ( x ) ≥ f ( x ) for each x in D . The function g is further said to be an upper bound of
280-592: The Rochester Jeffersons for the state championship . In 1919, it made the state playoffs but lost in the semifinals to the Buffalo Prospects , who went on to win the title. The 1920 All Tonawanda Lumberjacks were a very successful team, garnering a record of 7–1 against two local American Professional Football Association (the predecessor to the NFL) franchises and other independent teams, only allowing more than 6 points in one of their contests (the one loss,
300-676: The Rochester Jeffersons . There they played the worst game of their existence, a 45–0 blowout loss to the Jeffs in front of 2,700 fans. Several factors played into the Lumbermen's departure from the league. Records from the Pro Football Researchers Association indicate that Tonawanda had trouble scheduling games due to a lack of willing opponents. The now-renamed NFL's franchise fee for 1922 also increased from $ 50 to $ 1,000, making it harder for Tonawanda to play
320-475: The rational numbers may or may not be bounded from below, and may or may not be bounded from above. Every finite subset of a non-empty totally ordered set has both upper and lower bounds. The definitions can be generalized to functions and even to sets of functions. Given a function f with domain D and a preordered set ( K , ≤) as codomain , an element y of K is an upper bound of f if y ≥ f ( x ) for each x in D . The upper bound
340-441: The exact dates may not be known or may be in dispute. For example, consider an archaeological find of a burial that contains coins dating to 1588, 1595, and others less securely dated to 1590–1625. The terminus post quem for the burial would be the latest date established with certainty: in this case, 1595. A secure dating of an older coin to an earlier date would not shift the terminus post quem . An archaeological example of
360-412: The known limits of dating for events or items. A terminus post quem is the earliest date the event may have happened or the item was in existence, and a terminus ante quem is the latest. An event may well have both a terminus post quem and a terminus ante quem , in which case the limits of the possible range of dates are known at both ends, but many events have just one or the other. Similarly,
380-486: The mathematical literature for sets that have upper (respectively lower) bounds. For example, 5 is a lower bound for the set S = {5, 8, 42, 34, 13934} (as a subset of the integers or of the real numbers , etc.), and so is 4 . On the other hand, 6 is not a lower bound for S since it is not smaller than every element in S . 13934 and other numbers x such that x ≥ 13934 would be an upper bound for S . The set S = {42} has 42 as both an upper bound and
400-662: The nonexistent and spurious "Lumbermen Stadium" as the team's home field. The 1921 season began much like the first, with a scoreless tie against the Syracuse Pros , followed by a 9–7 win against the Cleveland Panthers . A game against the Rochester Scalpers scheduled for November was canceled; instead, on November 6, 1921, the Kardex traveled to Rochester to play their sole APFA league game, against
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