Ruzsa (“ROO-zhah”) names a distance function between these objects that can be used to prove a bound on sums of these objects called Plünnecke’s inequality. Functors from a locally small category into the category of these objects are the subject of the Yoneda lemma. A class is called “proper” if it is “too big” to be expressed as one of these objects. If X is one of these objects, then X has size strictly smaller than that of “two to the X” by Cantor’s theorem. Problems with constructing these objects via unrestricted comprehension were resolved with a theory of these objects named for Zermelo and Fraenkel that was later extended to include the axiom of choice. Countably infinite instances of these objects have cardinality equal to that of the natural numbers. For 10 points, name these unordered collections of elements. ■END■
| Northern California | Main | Y | 5 | 100% | 0% | 0% | 79.60 |
| Southern California | Main | Y | 6 | 100% | 0% | 0% | 81.17 |
| Florida | Main | Y | 6 | 100% | 0% | 0% | 97.33 |
| Great Lakes | Main | Y | 7 | 86% | 0% | 14% | 106.50 |
| Lower Mid-Atlantic | Main | Y | 10 | 100% | 0% | 10% | 109.00 |
| Upper Mid-Atlantic (1) | Main | Y | 10 | 100% | 0% | 20% | 109.90 |
| Upper Mid-Atlantic (2) | Main | Y | 5 | 80% | 0% | 0% | 101.75 |
| Upper Midwest | Main | Y | 9 | 100% | 0% | 0% | 84.22 |
| Upper Midwest | Main | Y | 1 | 100% | 0% | 0% | 104.00 |
| North | Main | Y | 5 | 100% | 0% | 0% | 99.80 |
| Northeast | Main | Y | 12 | 100% | 0% | 0% | 82.58 |
| Northwest | Main | Y | 4 | 100% | 0% | 25% | 81.25 |
| South Central | Main | Y | 8 | 100% | 0% | 0% | 92.38 |
| Southeast | Main | Y | 8 | 100% | 0% | 0% | 98.00 |
| UK | Main | Y | 11 | 100% | 0% | 0% | 72.45 |
| Upstate NY | Main | Y | 4 | 75% | 0% | 25% | 97.67 |
| Player | Team | Opponent | Buzz Position | Value |
|---|---|---|---|---|
| Skand Parvatikar | Arizona State A | Northwestern B | 22 | 10 |
| Nathan Sheffield | MIT A | Brown B | 23 | 10 |
| Agnijo Banerjee | Cambridge A | Manchester B | 35 | 10 |
| Kevin Ye | Simon Fraser | British Columbia C | 36 | 10 |
| Eric Lipsutz | Chicago D | Michigan A | 42 | 10 |
| Oliver West | Cambridge C | LSE A | 42 | 10 |
| Malachi Ledford | Tusculum | South Carolina A | 42 | 10 |
| Michael Zheng | Amherst A | Brown C | 42 | 10 |
| Abby Smith | Berkeley B | Stanford A | 42 | 10 |
| Swapnil Garg | Berkeley C | Berkeley F | 44 | 10 |
| Dmitri Anh-Minh Tran | UCSB | UCLA A | 47 | 10 |
| Anirudh Terdal | LSE B | Bristol A | 52 | 10 |
| Elijah Pollock | UTD A | Alberta B | 52 | 10 |
| Clio Selyuzhitsky | UCSD What Hath God Wrought | UCLA C | 53 | 10 |
| Philip Yao | Brown A | BC A | 55 | 10 |
| Odysseas Gabrielatos | Warwick B | Edinburgh B | 55 | 10 |
| Cade Reinberger | RIT B | Binghamton B | 58 | 10 |
| David Bass | Johns Hopkins A | Notre Dame E | 60 | 10 |
| Ishan Joshi | Rutgers B | Columbia B | 60 | 10 |
| Alex Akridge | Indiana A | Purdue C | 60 | 10 |
| Matthew Sumanen | Georgia Tech A | Alabama A | 60 | 10 |
| Matthew Wang | British Columbia D | Washington A | 60 | 10 |
| Alexander Mayans | Arizona State B | Northwestern A | 60 | 10 |
| Alec Riso | Cornell-UG | Bowdoin B | 62 | 10 |
| Will Huang | Wisconsin | Minnesota B | 67 | 10 |
| Artem Borisov | Bristol B | Lancaster A | 80 | 10 |
| Will McCurley | Auburn A | Georgia Tech B | 82 | 10 |
| Vincent Zhang | Penn A | Maryland B | 82 | 10 |
| Jeevan Iyadurai | UF E | Melbourne B | 83 | 10 |
| Jake Meltzer | CWRU A | MSU A | 83 | 10 |
| Akshar Goyal | Illinois A | Indiana B | 83 | 10 |
| Rayhana Amjad | Edinburgh A | Imperial B | 83 | 10 |
| Eveline Ong | Oxford A | Imperial C | 83 | 10 |
| Andrew Nucci | UCLA B | UCSD Vices and Virtues | 83 | 10 |
| Mattias Ehatamm | Maryland A | George Mason C | 83 | -5 |
| Sidarth Erat | MIT B | Dartmouth | 83 | 10 |
| Matthew Kohn | Williams | Bowdoin A | 83 | 10 |
| Alvin Guo | Chicago A | Michigan D | 83 | 10 |
| Varun Sathyajeeth | OSU C | OSU A | 84 | 10 |
| Aryan Pathak | UF C | ERAU A | 85 | 10 |
| Wyatt Johnson | CWRU B | OSU D | 86 | 10 |
| Brayden Zhang | Vanderbilt B | Georgia Tech D | 86 | 10 |
| Hiru Senehedheera | Manchester A | Southampton A | 86 | 10 |
| Ben Richards | Sheffield B | Birmingham A | 88 | 10 |
| Nick Fowler | Virginia B | Roanoke | 88 | 10 |
| Alex Olson | UF D | FSU | 89 | 10 |
| James Wong | Cambridge B | Imperial A | 89 | 10 |
| Nishad Joshi | Kentucky | Notre Dame D | 89 | 10 |
| Puna Ekka | Minnesota A | Macalester A | 90 | 10 |
| Jack Casey | Illinois B | Purdue A | 91 | 10 |
| Tai Belke | British Columbia A | Washington B | 91 | 10 |
| Jonathan Ho | Alberta | British Columbia B | 91 | -5 |
| Scott Sibley | UCI | UCLA D | 93 | 10 |
| Sam Kemeny | Brandeis Clemenceau | Yale A | 93 | 10 |
| Jacob Chambers | Iowa State | Macalester B | 99 | 10 |
| Aidan Keenan | Rochester | RIT A | 99 | 10 |
| Osbaldo Porrua | UIC | Notre Dame B | 101 | 10 |
| Jacob Finley | Notre Dame A | Purdue B | 102 | 10 |
| Jack Lewis | Bruin A | Huntsville B | 102 | 10 |
| Liam Rojas | Virginia A | NC State | 102 | 10 |
| Will Zhang | Tufts A | Amherst B | 102 | 10 |
| June Miller | UF B | ERAU B | 103 | 10 |
| Matthew Andersen | UF A | USF | 103 | 10 |
| Karthik Krishnamurthy | USC | Claremont Pitzer | 104 | 10 |
| Ian Parsons | Maryland D | Penn B | 104 | 10 |
| Ben Hellman | Swarthmore A | Columbia C | 104 | 10 |
| Samuel Lipsutz | Chicago C | Notre Dame C | 104 | 10 |
| Sawyer Smith | Mississippi State A | Sewanee A | 104 | 10 |
| Coy Mier | Auburn B | UAB A | 104 | 10 |
| Rufus Gladwell | Durham B | Sheffield C | 104 | 10 |
| Lorie Au Yeung | UCSC | Stanford B | 104 | 10 |
| Eshan Pant | NYU A | Catholic University | 104 | 10 |
| Rohan Ganeshan | Harvard | Yale B | 104 | 10 |
| Young Fenimore Lee | Ohio | Tulsa | 104 | 10 |
| Ryan Sun | Berkeley D | Berkeley A | 104 | 10 |
| Vikram Narasimhan | Stanford C | Berkeley E | 104 | 10 |
| Isaac Studley | Carleton | Minnesota C | 104 | 10 |
| Nghia Khau | VCU A | UMBC A | 105 | 10 |
| Zachary Joseph | Columbia A | Princeton A | 105 | 10 |
| Henry Nonnemaker | CWRU C | Kenyon A | 107 | -5 |
| March Delfin | UCSD Two Running Violet V Forms | Claremont Scripps | 107 | 10 |
| Rohit Chintala | Maryland C | Georgetown B | 107 | -5 |
| Dennis Yang | Michigan B | Louisville B | 107 | 10 |
| Jacob Evans | MSU B | OSU B | 108 | 10 |
| Gavin Markoff | Vanderbilt A | Huntsville A | 108 | 10 |
| Jim Fan | North Carolina A | South Carolina B | 108 | 10 |
| Devon Kumar | Tufts B | Brandeis Wilson | 108 | 10 |
| Jisoo Yoo | Texas B | Northwestern C | 109 | 10 |
| Zaid Asif | NYU B | George Washington B | 114 | 10 |
| Vayun Krishna | Georgetown A | George Mason B | 114 | 10 |
| Nikhil Nair | BU | Brandeis Orlando | 114 | 10 |
| Randy Guo | Texas A | McGill D | 114 | 10 |
| Claire Chambers | Binghamton A | Syracuse | 115 | -5 |
| Hayden Owen | Clemson A | Virginia Tech A | 117 | 10 |
| Josh Schmidt | Liberty A | Tennessee B | 120 | 10 |
| Sam Kung | North Carolina C | Liberty C | 120 | 10 |
| Mateo Acosta | FIU | Melbourne A | 121 | 10 |
| Michael Sun | Brandeis Lloyd George | BC B | 122 | 10 |
| Nick Smemoe | North Carolina B | James Madison | 125 | 10 |
| Asheton Wilbanks | Clemson B | Tennessee A | 129 | 10 |
| Jaden Rupolo | Liberty B | Virginia Tech B | 129 | -5 |
| Pranaav Senthilkumar | Cornell-DII | ESF | 136 | 10 |
| Chase Barrick | Lehigh A | Vassar A | 138 | 10 |
| Monish Jampala | Georgia Tech C | Alabama B | 138 | 10 |
| Gabriel Avrahami | Georgetown B | Maryland C | 138 | 10 |
| John Chen | British Columbia B | Alberta | 138 | 10 |
| Graham Price | Kenyon A | CWRU C | 139 | 0 |
| Mohit Nair | CWRU D | Kenyon B | 139 | 10 |
| John Shelly | Rowan A | Lehigh B | 139 | 0 |
| Vincent Chen | Pitt B | Pitt C | 139 | 10 |
| Kevin Cronk | Virginia Tech B | Liberty B | 139 | 10 |
| Lesley Kwarteng | Johns Hopkins C | George Washington A | 139 | 10 |
| Anubhav Kamath | George Mason C | Maryland A | 139 | 10 |
| Cassidy McIntyre | Rose State | Iowa | 139 | 0 |
| Brielle Rach | Iowa | Rose State | 139 | 10 |
| Collin Leck | UCO | UTD B | 139 | 10 |
| Connor King | St. Thomas | Nebraska | 139 | 10 |
| Caitlyn Begosa | Syracuse | Binghamton A | 139 | 0 |