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 |
| Abby Smith | Berkeley B | Stanford A | 42 | 10 |
| Michael Zheng | Amherst A | Brown C | 42 | 10 |
| Oliver West | Cambridge C | LSE A | 42 | 10 |
| Malachi Ledford | Tusculum | South Carolina A | 42 | 10 |
| Eric Lipsutz | Chicago D | Michigan A | 42 | 10 |
| Swapnil Garg | Berkeley C | Berkeley F | 44 | 10 |
| Dmitri Anh-Minh Tran | UCSB | UCLA A | 47 | 10 |
| Elijah Pollock | UTD A | Alberta B | 52 | 10 |
| Anirudh Terdal | LSE B | Bristol A | 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 |
| 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 |
| Alex Akridge | Indiana A | Purdue C | 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 |
| Andrew Nucci | UCLA B | UCSD Vices and Virtues | 83 | 10 |
| Jeevan Iyadurai | UF E | Melbourne B | 83 | 10 |
| Jake Meltzer | CWRU A | MSU A | 83 | 10 |
| Alvin Guo | Chicago A | Michigan D | 83 | 10 |
| Matthew Kohn | Williams | Bowdoin A | 83 | 10 |
| Eveline Ong | Oxford A | Imperial C | 83 | 10 |
| Sidarth Erat | MIT B | Dartmouth | 83 | 10 |
| Rayhana Amjad | Edinburgh A | Imperial B | 83 | 10 |
| Mattias Ehatamm | Maryland A | George Mason C | 83 | -5 |
| Akshar Goyal | Illinois A | Indiana B | 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 |
| Nick Fowler | Virginia B | Roanoke | 88 | 10 |
| Ben Richards | Sheffield B | Birmingham A | 88 | 10 |
| Nishad Joshi | Kentucky | Notre Dame D | 89 | 10 |
| James Wong | Cambridge B | Imperial A | 89 | 10 |
| Alex Olson | UF D | FSU | 89 | 10 |
| Puna Ekka | Minnesota A | Macalester A | 90 | 10 |
| Jonathan Ho | Alberta | British Columbia B | 91 | -5 |
| Tai Belke | British Columbia A | Washington B | 91 | 10 |
| Jack Casey | Illinois B | Purdue A | 91 | 10 |
| 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 |
| Will Zhang | Tufts A | Amherst B | 102 | 10 |
| Jack Lewis | Bruin A | Huntsville B | 102 | 10 |
| Liam Rojas | Virginia A | NC State | 102 | 10 |
| Jacob Finley | Notre Dame A | Purdue B | 102 | 10 |
| June Miller | UF B | ERAU B | 103 | 10 |
| Matthew Andersen | UF A | USF | 103 | 10 |
| Ryan Sun | Berkeley D | Berkeley A | 104 | 10 |
| Vikram Narasimhan | Stanford C | Berkeley E | 104 | 10 |
| Karthik Krishnamurthy | USC | Claremont Pitzer | 104 | 10 |
| Ian Parsons | Maryland D | Penn B | 104 | 10 |
| Isaac Studley | Carleton | Minnesota C | 104 | 10 |
| Rohan Ganeshan | Harvard | Yale B | 104 | 10 |
| Young Fenimore Lee | Ohio | Tulsa | 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 |
| Ben Hellman | Swarthmore A | Columbia C | 104 | 10 |
| Samuel Lipsutz | Chicago C | Notre Dame C | 104 | 10 |
| Nghia Khau | VCU A | UMBC A | 105 | 10 |
| Zachary Joseph | Columbia A | Princeton A | 105 | 10 |
| March Delfin | UCSD Two Running Violet V Forms | Claremont Scripps | 107 | 10 |
| Henry Nonnemaker | CWRU C | Kenyon A | 107 | -5 |
| Rohit Chintala | Maryland C | Georgetown B | 107 | -5 |
| Dennis Yang | Michigan B | Louisville B | 107 | 10 |
| Jacob Evans | MSU B | OSU B | 108 | 10 |
| Devon Kumar | Tufts B | Brandeis Wilson | 108 | 10 |
| Gavin Markoff | Vanderbilt A | Huntsville A | 108 | 10 |
| Jim Fan | North Carolina A | South Carolina B | 108 | 10 |
| Jisoo Yoo | Texas B | Northwestern C | 109 | 10 |
| Vayun Krishna | Georgetown A | George Mason B | 114 | 10 |
| Zaid Asif | NYU B | George Washington 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 |
| Gabriel Avrahami | Georgetown B | Maryland C | 138 | 10 |
| Chase Barrick | Lehigh A | Vassar A | 138 | 10 |
| John Chen | British Columbia B | Alberta | 138 | 10 |
| Monish Jampala | Georgia Tech C | Alabama B | 138 | 10 |
| Graham Price | Kenyon A | CWRU C | 139 | 0 |
| Mohit Nair | CWRU D | Kenyon B | 139 | 10 |
| Vincent Chen | Pitt B | Pitt C | 139 | 10 |
| Kevin Cronk | Virginia Tech B | Liberty B | 139 | 10 |
| John Shelly | Rowan A | Lehigh B | 139 | 0 |
| Connor King | St. Thomas | Nebraska | 139 | 10 |
| Collin Leck | UCO | UTD B | 139 | 10 |
| Caitlyn Begosa | Syracuse | Binghamton A | 139 | 0 |
| Cassidy McIntyre | Rose State | Iowa | 139 | 0 |
| Brielle Rach | Iowa | Rose State | 139 | 10 |
| Lesley Kwarteng | Johns Hopkins C | George Washington A | 139 | 10 |
| Anubhav Kamath | George Mason C | Maryland A | 139 | 10 |