Question
A form of this inequality named for Imre Ruzsa states that for sets A, B, and C, cardinality of B times cardinality of A minus C is at most cardinality of A minus B times cardinality of B minus C. For 10 points each:
[10e] Name this inequality. In its simplest form, this inequality states that the magnitude of x plus y is less than or equal to the magnitude of x plus the magnitude of y.
ANSWER: triangle inequality [accept Rusza triangle inequality]
[10m] The Ruzsa triangle inequality motivates the definition of a function named for Rusza that is almost one of these functions. These functions are positive definite, symmetric, and satisfy the triangle inequality.
ANSWER: metrics [or distance functions; prompt on d]
[10h] The Rusza distance serves much the same purpose as a measure Tao and Vu named for an "additive" form of this concept. This concept names methods to prove the uniqueness of a solution to a PDE in which a quantity is proved to be nonnegative, nonincreasing, and zero at time zero.
ANSWER: energy [accept additive energy or energy methods] (According to a Terence Tao StackExchange post, additive energy and energy in the context of PDEs are not as unrelated as one might think.)
<Science - Other Science - Math>
Summary
| 2024 ARGOS @ Brandeis | 03/22/2025 | Y | 3 | 6.67 | 33% | 33% | 0% |
| 2024 ARGOS @ Chicago | 11/23/2024 | Y | 6 | 18.33 | 100% | 67% | 17% |
| 2024 ARGOS @ Christ's College | 12/14/2024 | Y | 3 | 23.33 | 67% | 100% | 67% |
| 2024 ARGOS @ Columbia | 11/23/2024 | Y | 4 | 30.00 | 200% | 0% | 100% |
| 2024 ARGOS @ McMaster | 11/17/2024 | Y | 5 | 14.00 | 60% | 60% | 20% |
| 2024 ARGOS @ Stanford | 02/22/2025 | Y | 3 | 20.00 | 100% | 67% | 33% |
| 2024 ARGOS Online | 03/22/2025 | Y | 3 | 16.67 | 100% | 67% | 0% |
Data
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