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 |
| Eric Lipsutz | Chicago D | Michigan 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 |
| Matthew Wang | British Columbia D | Washington A | 60 | 10 |
| Alexander Mayans | Arizona State B | Northwestern A | 60 | 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 |
| 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 |
| Jake Meltzer | CWRU A | MSU A | 83 | 10 |
| Sidarth Erat | MIT B | Dartmouth | 83 | 10 |
| Matthew Kohn | Williams | Bowdoin A | 83 | 10 |
| Eveline Ong | Oxford A | Imperial C | 83 | 10 |
| Akshar Goyal | Illinois A | Indiana B | 83 | 10 |
| Alvin Guo | Chicago A | Michigan D | 83 | 10 |
| Andrew Nucci | UCLA B | UCSD Vices and Virtues | 83 | 10 |
| Jeevan Iyadurai | UF E | Melbourne B | 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 |
| Sam Kemeny | Brandeis Clemenceau | Yale A | 93 | 10 |
| Scott Sibley | UCI | UCLA D | 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 |
| 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 |
| 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 |
| Rohan Ganeshan | Harvard | Yale B | 104 | 10 |
| Young Fenimore Lee | Ohio | Tulsa | 104 | 10 |
| Lorie Au Yeung | UCSC | Stanford B | 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 |
| Isaac Studley | Carleton | Minnesota C | 104 | 10 |
| Karthik Krishnamurthy | USC | Claremont Pitzer | 104 | 10 |
| Eshan Pant | NYU A | Catholic University | 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 |
| Henry Nonnemaker | CWRU C | Kenyon A | 107 | -5 |
| Dennis Yang | Michigan B | Louisville B | 107 | 10 |
| March Delfin | UCSD Two Running Violet V Forms | Claremont Scripps | 107 | 10 |
| Rohit Chintala | Maryland C | Georgetown B | 107 | -5 |
| Jacob Evans | MSU B | OSU B | 108 | 10 |
| Devon Kumar | Tufts B | Brandeis Wilson | 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 |
| Nikhil Nair | BU | Brandeis Orlando | 114 | 10 |
| Zaid Asif | NYU B | George Washington B | 114 | 10 |
| Vayun Krishna | Georgetown A | George Mason B | 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 |
| John Chen | British Columbia B | Alberta | 138 | 10 |
| Chase Barrick | Lehigh A | Vassar A | 138 | 10 |
| Gabriel Avrahami | Georgetown B | Maryland C | 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 |
| Cassidy McIntyre | Rose State | Iowa | 139 | 0 |
| Brielle Rach | Iowa | Rose State | 139 | 10 |
| Caitlyn Begosa | Syracuse | Binghamton A | 139 | 0 |
| Vincent Chen | Pitt B | Pitt C | 139 | 10 |
| John Shelly | Rowan A | Lehigh B | 139 | 0 |
| Connor King | St. Thomas | Nebraska | 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 |
| Collin Leck | UCO | UTD B | 139 | 10 |