query: Computational complexity proof
positive_passages.docid: 16798
positive_passages.text: Prove the inequality $n! \geq 2^n$ by induction
negative_passages.docid: 154038
negative_passages.text: A constructive lower bound on Ramsey numbers
negative_passages.docid: 27356
negative_passages.text: Lower bound on proof length
negative_passages.docid: 131132
negative_passages.text: Proofs using vector properties
negative_passages.docid: 25064
negative_passages.text: Proving the snake lemma without a diagram chase
negative_passages.docid: 15452
negative_passages.text: Proving determinant product rule combinatorially
negative_passages.docid: 78359
negative_passages.text: Induction and Recursion Proof using Catalan Numbers
negative_passages.docid: 65168
negative_passages.text: Proof of sequence inequality
negative_passages.docid: 124901
negative_passages.text: Big-O notation and polynomials
negative_passages.docid: 145447
negative_passages.text: bilinear form - proof
negative_passages.docid: 41726
negative_passages.text: Musical and combinatorial proof
negative_passages.docid: 146984
negative_passages.text: Prove: Full Rank and a solution os linear system
negative_passages.docid: 46430
negative_passages.text: A simple decision problem whose decidability is not known
negative_passages.docid: 122998
negative_passages.text: number of edges induction proof
negative_passages.docid: 24212
negative_passages.text: proving how many permutations exist.
negative_passages.docid: 72371
negative_passages.text: Proof of Strong Induction Using Well-Ordering Principle
negative_passages.docid: 75141
negative_passages.text: Quotient-Remainder Theorem Proving