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Invariants in mathematics 본문
Summary.
- Invariants are important tools for proving impossibility, termination, and various bounds.
- Invariants may take many forms: numbers, "parity", equations, inequalities.
- To prove impossibility, one finds a quantity that never changes during a process.
- To prove that a process terminates in a number of steps, one usually finds a quantity that decreases at every step.
- Double counting is a method that uses the sum invariant.
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