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 |
| Michael Zheng | Amherst A | Brown C | 42 | 10 |
| Eric Lipsutz | Chicago D | Michigan A | 42 | 10 |
| Abby Smith | Berkeley B | Stanford A | 42 | 10 |
| Malachi Ledford | Tusculum | South Carolina A | 42 | 10 |
| Oliver West | Cambridge C | LSE 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 |
| Matthew Wang | British Columbia D | Washington A | 60 | 10 |
| Alexander Mayans | Arizona State B | Northwestern A | 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 |
| Alec Riso | Cornell-UG | Bowdoin B | 62 | 10 |
| Will Huang | Wisconsin | Minnesota B | 67 | 10 |
| Artem Borisov | Bristol B | Lancaster A | 80 | 10 |
| Vincent Zhang | Penn A | Maryland B | 82 | 10 |
| Will McCurley | Auburn A | Georgia Tech B | 82 | 10 |
| Andrew Nucci | UCLA B | UCSD Vices and Virtues | 83 | 10 |
| Sidarth Erat | MIT B | Dartmouth | 83 | 10 |
| Matthew Kohn | Williams | Bowdoin A | 83 | 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 |
| Alvin Guo | Chicago A | Michigan D | 83 | 10 |
| Eveline Ong | Oxford A | Imperial C | 83 | 10 |
| Mattias Ehatamm | Maryland A | George Mason C | 83 | -5 |
| Rayhana Amjad | Edinburgh A | Imperial 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 |
| Alex Olson | UF D | FSU | 89 | 10 |
| Nishad Joshi | Kentucky | Notre Dame D | 89 | 10 |
| James Wong | Cambridge B | Imperial A | 89 | 10 |
| Puna Ekka | Minnesota A | Macalester A | 90 | 10 |
| Tai Belke | British Columbia A | Washington B | 91 | 10 |
| Jonathan Ho | Alberta | British Columbia B | 91 | -5 |
| 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 |
| Jacob Finley | Notre Dame A | Purdue B | 102 | 10 |
| Liam Rojas | Virginia A | NC State | 102 | 10 |
| Jack Lewis | Bruin A | Huntsville B | 102 | 10 |
| June Miller | UF B | ERAU B | 103 | 10 |
| Matthew Andersen | UF A | USF | 103 | 10 |
| Lorie Au Yeung | UCSC | Stanford B | 104 | 10 |
| Ian Parsons | Maryland D | Penn B | 104 | 10 |
| Rohan Ganeshan | Harvard | Yale B | 104 | 10 |
| Young Fenimore Lee | Ohio | Tulsa | 104 | 10 |
| Karthik Krishnamurthy | USC | Claremont Pitzer | 104 | 10 |
| Samuel Lipsutz | Chicago C | Notre Dame C | 104 | 10 |
| Isaac Studley | Carleton | Minnesota C | 104 | 10 |
| Ryan Sun | Berkeley D | Berkeley A | 104 | 10 |
| Vikram Narasimhan | Stanford C | Berkeley E | 104 | 10 |
| Eshan Pant | NYU A | Catholic University | 104 | 10 |
| Ben Hellman | Swarthmore A | Columbia 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 |
| 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 |
| Jacob Evans | MSU B | OSU B | 108 | 10 |
| Jim Fan | North Carolina A | South Carolina B | 108 | 10 |
| Gavin Markoff | Vanderbilt A | Huntsville A | 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 |
| John Chen | British Columbia B | Alberta | 138 | 10 |
| Chase Barrick | Lehigh A | Vassar A | 138 | 10 |
| Monish Jampala | Georgia Tech C | Alabama B | 138 | 10 |
| Vincent Chen | Pitt B | Pitt C | 139 | 10 |
| Kevin Cronk | Virginia Tech B | Liberty B | 139 | 10 |
| Cassidy McIntyre | Rose State | Iowa | 139 | 0 |
| Brielle Rach | Iowa | Rose State | 139 | 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 |
| Connor King | St. Thomas | Nebraska | 139 | 10 |
| Caitlyn Begosa | Syracuse | Binghamton A | 139 | 0 |
| Lesley Kwarteng | Johns Hopkins C | George Washington A | 139 | 10 |
| Anubhav Kamath | George Mason C | Maryland A | 139 | 10 |
| Collin Leck | UCO | UTD B | 139 | 10 |