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 |
| Eric Lipsutz | Chicago D | Michigan A | 42 | 10 |
| Oliver West | Cambridge C | LSE A | 42 | 10 |
| Michael Zheng | Amherst A | Brown C | 42 | 10 |
| Malachi Ledford | Tusculum | South Carolina 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 |
| 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 |
| Vincent Zhang | Penn A | Maryland B | 82 | 10 |
| Will McCurley | Auburn A | Georgia Tech B | 82 | 10 |
| Mattias Ehatamm | Maryland A | George Mason C | 83 | -5 |
| Akshar Goyal | Illinois A | Indiana B | 83 | 10 |
| Alvin Guo | Chicago A | Michigan D | 83 | 10 |
| Eveline Ong | Oxford A | Imperial C | 83 | 10 |
| Andrew Nucci | UCLA B | UCSD Vices and Virtues | 83 | 10 |
| Jeevan Iyadurai | UF E | Melbourne B | 83 | 10 |
| Sidarth Erat | MIT B | Dartmouth | 83 | 10 |
| Matthew Kohn | Williams | Bowdoin A | 83 | 10 |
| Rayhana Amjad | Edinburgh A | Imperial B | 83 | 10 |
| Jake Meltzer | CWRU A | MSU A | 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 |
| Hiru Senehedheera | Manchester A | Southampton A | 86 | 10 |
| Wyatt Johnson | CWRU B | OSU D | 86 | 10 |
| Ben Richards | Sheffield B | Birmingham A | 88 | 10 |
| Nick Fowler | Virginia B | Roanoke | 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 |
| Jonathan Ho | Alberta | British Columbia B | 91 | -5 |
| Jack Casey | Illinois B | Purdue A | 91 | 10 |
| Tai Belke | British Columbia A | Washington B | 91 | 10 |
| Scott Sibley | UCI | UCLA D | 93 | 10 |
| Sam Kemeny | Brandeis Clemenceau | Yale A | 93 | 10 |
| Aidan Keenan | Rochester | RIT A | 99 | 10 |
| Jacob Chambers | Iowa State | Macalester B | 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 |
| Matthew Andersen | UF A | USF | 103 | 10 |
| June Miller | UF B | ERAU B | 103 | 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 |
| Ian Parsons | Maryland D | Penn B | 104 | 10 |
| Ben Hellman | Swarthmore A | Columbia C | 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 |
| 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 |
| Nghia Khau | VCU A | UMBC A | 105 | 10 |
| Zachary Joseph | Columbia A | Princeton A | 105 | 10 |
| Dennis Yang | Michigan B | Louisville B | 107 | 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 |
| 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 |
| Zaid Asif | NYU B | George Washington B | 114 | 10 |
| Randy Guo | Texas A | McGill D | 114 | 10 |
| Nikhil Nair | BU | Brandeis Orlando | 114 | 10 |
| Vayun Krishna | Georgetown A | George Mason B | 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 |
| John Chen | British Columbia B | Alberta | 138 | 10 |
| Monish Jampala | Georgia Tech C | Alabama B | 138 | 10 |
| Gabriel Avrahami | Georgetown B | Maryland C | 138 | 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 |
| Collin Leck | UCO | UTD B | 139 | 10 |
| Caitlyn Begosa | Syracuse | Binghamton A | 139 | 0 |
| Connor King | St. Thomas | Nebraska | 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 |
| Vincent Chen | Pitt B | Pitt C | 139 | 10 |
| Kevin Cronk | Virginia Tech B | Liberty B | 139 | 10 |