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 |
| Abby Smith | Berkeley B | Stanford A | 42 | 10 |
| Malachi Ledford | Tusculum | South Carolina A | 42 | 10 |
| Michael Zheng | Amherst A | Brown C | 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 |
| Alex Akridge | Indiana A | Purdue C | 60 | 10 |
| Matthew Wang | British Columbia D | Washington A | 60 | 10 |
| David Bass | Johns Hopkins A | Notre Dame E | 60 | 10 |
| Alexander Mayans | Arizona State B | Northwestern A | 60 | 10 |
| Matthew Sumanen | Georgia Tech A | Alabama A | 60 | 10 |
| Ishan Joshi | Rutgers B | Columbia B | 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 |
| Akshar Goyal | Illinois A | Indiana B | 83 | 10 |
| Sidarth Erat | MIT B | Dartmouth | 83 | 10 |
| Jake Meltzer | CWRU A | MSU A | 83 | 10 |
| Mattias Ehatamm | Maryland A | George Mason C | 83 | -5 |
| Alvin Guo | Chicago A | Michigan D | 83 | 10 |
| Matthew Kohn | Williams | Bowdoin A | 83 | 10 |
| Rayhana Amjad | Edinburgh A | Imperial B | 83 | 10 |
| Eveline Ong | Oxford A | Imperial C | 83 | 10 |
| Varun Sathyajeeth | OSU C | OSU A | 84 | 10 |
| Aryan Pathak | UF C | ERAU A | 85 | 10 |
| Brayden Zhang | Vanderbilt B | Georgia Tech D | 86 | 10 |
| Wyatt Johnson | CWRU B | OSU 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 |
| Will Zhang | Tufts A | Amherst B | 102 | 10 |
| Jack Lewis | Bruin A | Huntsville B | 102 | 10 |
| Liam Rojas | Virginia A | NC State | 102 | 10 |
| June Miller | UF B | ERAU B | 103 | 10 |
| Matthew Andersen | UF A | USF | 103 | 10 |
| Karthik Krishnamurthy | USC | Claremont Pitzer | 104 | 10 |
| Samuel Lipsutz | Chicago C | Notre Dame C | 104 | 10 |
| Ian Parsons | Maryland D | Penn 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 |
| Ryan Sun | Berkeley D | Berkeley A | 104 | 10 |
| Vikram Narasimhan | Stanford C | Berkeley E | 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 |
| Isaac Studley | Carleton | Minnesota C | 104 | 10 |
| Rohan Ganeshan | Harvard | Yale B | 104 | 10 |
| Rufus Gladwell | Durham B | Sheffield 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 |
| Rohit Chintala | Maryland C | Georgetown B | 107 | -5 |
| Henry Nonnemaker | CWRU C | Kenyon A | 107 | -5 |
| Dennis Yang | Michigan B | Louisville B | 107 | 10 |
| Devon Kumar | Tufts B | Brandeis Wilson | 108 | 10 |
| Gavin Markoff | Vanderbilt A | Huntsville A | 108 | 10 |
| Jacob Evans | MSU B | OSU B | 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 |
| Randy Guo | Texas A | McGill D | 114 | 10 |
| Nikhil Nair | BU | Brandeis Orlando | 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 |
| Jaden Rupolo | Liberty B | Virginia Tech B | 129 | -5 |
| Asheton Wilbanks | Clemson B | Tennessee A | 129 | 10 |
| Pranaav Senthilkumar | Cornell-DII | ESF | 136 | 10 |
| Gabriel Avrahami | Georgetown B | Maryland C | 138 | 10 |
| Monish Jampala | Georgia Tech C | Alabama B | 138 | 10 |
| Chase Barrick | Lehigh A | Vassar A | 138 | 10 |
| John Chen | British Columbia B | Alberta | 138 | 10 |
| Kevin Cronk | Virginia Tech B | Liberty B | 139 | 10 |
| Cassidy McIntyre | Rose State | Iowa | 139 | 0 |
| Brielle Rach | Iowa | Rose State | 139 | 10 |
| Collin Leck | UCO | UTD B | 139 | 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 |
| Lesley Kwarteng | Johns Hopkins C | George Washington A | 139 | 10 |
| Anubhav Kamath | George Mason C | Maryland A | 139 | 10 |
| John Shelly | Rowan A | Lehigh B | 139 | 0 |
| Connor King | St. Thomas | Nebraska | 139 | 10 |
| Caitlyn Begosa | Syracuse | Binghamton A | 139 | 0 |