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■
| 2024 ARCADIA at UC Berkeley | 04/19/2025 | Y | 4 | 75% | 0% | 25% | 97.67 |
| 2025 ACF Nationals | 2025-08-09 | Y | 11 | 100% | 0% | 0% | 72.45 |
| Great Lakes | Main | Y | 6 | 100% | 0% | 0% | 97.33 |
| Lower Mid-Atlantic | Main | Y | 7 | 86% | 0% | 14% | 106.50 |
| Midwest | Main | Y | 10 | 100% | 0% | 10% | 109.00 |
| North | Main | Y | 10 | 100% | 0% | 20% | 109.90 |
| Northeast | Main | Y | 5 | 80% | 0% | 0% | 101.75 |
| Pacific Northwest | Main | Y | 9 | 100% | 0% | 0% | 84.22 |
| California | Main | Y | 5 | 100% | 0% | 0% | 79.60 |
| South Central | Main | Y | 5 | 100% | 0% | 0% | 99.80 |
| Southeast | Main | Y | 12 | 100% | 0% | 0% | 82.58 |
| UK | Main | Y | 4 | 100% | 0% | 25% | 81.25 |
| Upper Mid-Atlantic | Main | Y | 8 | 100% | 0% | 0% | 92.38 |
| Upstate NY | Main | Y | 8 | 100% | 0% | 0% | 98.00 |
| Pacific Northwest | Main | Y | 1 | 100% | 0% | 0% | 104.00 |
| Canada | Main | Y | 6 | 100% | 0% | 0% | 81.17 |
| 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 |
| Malachi Ledford | Tusculum | South Carolina A | 42 | 10 |
| Eric Lipsutz | Chicago D | Michigan A | 42 | 10 |
| Michael Zheng | Amherst A | Brown C | 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 |
| Ishan Joshi | Rutgers B | Columbia B | 60 | 10 |
| Alex Akridge | Indiana A | Purdue C | 60 | 10 |
| Matthew Wang | British Columbia D | Washington A | 60 | 10 |
| Alexander Mayans | Arizona State B | Northwestern A | 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 |
| Jeevan Iyadurai | UF E | Melbourne B | 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 |
| Akshar Goyal | Illinois A | Indiana B | 83 | 10 |
| Matthew Kohn | Williams | Bowdoin A | 83 | 10 |
| Sidarth Erat | MIT B | Dartmouth | 83 | 10 |
| Eveline Ong | Oxford A | Imperial C | 83 | 10 |
| 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 |
| Jack Casey | Illinois B | Purdue A | 91 | 10 |
| Jonathan Ho | Alberta | British Columbia B | 91 | -5 |
| Tai Belke | British Columbia A | Washington B | 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 |
| Liam Rojas | Virginia A | NC State | 102 | 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 |
| Matthew Andersen | UF A | USF | 103 | 10 |
| June Miller | UF B | ERAU B | 103 | 10 |
| Ryan Sun | Berkeley D | Berkeley A | 104 | 10 |
| Lorie Au Yeung | UCSC | Stanford B | 104 | 10 |
| Vikram Narasimhan | Stanford C | Berkeley E | 104 | 10 |
| Karthik Krishnamurthy | USC | Claremont Pitzer | 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 |
| 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 |
| 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 |
| Jim Fan | North Carolina A | South Carolina B | 108 | 10 |
| Devon Kumar | Tufts B | Brandeis Wilson | 108 | 10 |
| Gavin Markoff | Vanderbilt A | Huntsville A | 108 | 10 |
| Jisoo Yoo | Texas B | Northwestern C | 109 | 10 |
| Zaid Asif | NYU B | George Washington B | 114 | 10 |
| Vayun Krishna | Georgetown A | George Mason 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 |
| Sam Kung | North Carolina C | Liberty C | 120 | 10 |
| Josh Schmidt | Liberty A | Tennessee B | 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 |
| 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 |
| Anubhav Kamath | George Mason C | Maryland A | 139 | 10 |
| Lesley Kwarteng | Johns Hopkins C | George Washington A | 139 | 10 |
| John Shelly | Rowan A | Lehigh B | 139 | 0 |
| Connor King | St. Thomas | Nebraska | 139 | 10 |
| Cassidy McIntyre | Rose State | Iowa | 139 | 0 |
| Brielle Rach | Iowa | Rose State | 139 | 10 |
| Collin Leck | UCO | UTD B | 139 | 10 |
| Caitlyn Begosa | Syracuse | Binghamton A | 139 | 0 |