induction n. 1.就职,入伍,接纳会员,就职仪式 2.吸入 3.(电或磁的)感应 4.归纳(法) 5.催产;催生 proof 保护;防御;不能透过;同…一样 Proof n. 证据,证明,试验,检验,考验 a. 不能透入的,证明用的,防…的 proof n. 1.[U,C]证据,证明 2.[U]检验,证实 3.[C]【数学】证明,求证,验算 4...
3. 寻找反例 (Proof by Counterexample / Counterclaim) Example 2: 4. 归纳法 (Proof by Induction) Example 6: Example 7: 总结 在数学AA课程大纲中,所有会考到的证明方法在课本中被归为四种: 直接证明 (Direct Proof) 反证法 (Proof by Contradiction) 寻找反例 (Counterexample / Counterclaim) 归纳法 (Pro...
Algorithms Appendix I: Proof by Induction [Fa’13] Proof by smallest counterexample: For the sake of argument, assume that there is an integer greater than 1 with no prime divisor. Let n be the smallest integer greater than 1 with no prime divisor. Since n is a divisor of n, and n ...
n 1.(Logic) a method of disproving a proposition by showing that its inevitable consequences would be absurd 2.(Logic) a method of indirectly proving a proposition by assuming its negation to be true and showing that this leads to an absurdity ...
beingk+ 1. Suppose we are successful in this, and that we can show that (*) does in fact work at a specific (non-generic) number (let's stick withn= 1). Then, by induction, we know that (*) works at2and, by induction, it works at3and, by induction, it works at4, and so...
上面代码中的第一行关键字[intros],用于普遍量化的变量n,m移入证明的上下文中,这和前面Proof By Simpication中的[intros]关键字的作用一样。 第二行中的[intros H]用于将推论中的假设[n = m]并为其命名为H。 第三行中的关键字[rewrite]用于告诉Coq重写当前目标([n + n = m + m])。将目标中出现的...
At this point, to be able to show that n is divisible by 3, we need to prove that 10s−1 is divisible by 3 for all s≥ 1. This is the step that can require proof by induction (see Exercise 38 at the end of the section on Mathematical Induction) unless one is familiar with mo...
TWO EXAMPLES OF PROOF BY MATHEMATICAL INDUCTION.DR. LOMONACOProposition: Use the principle of mathematical induction to prove that P (n) :nΣj=1j2 = n(n + 1) (2n + 1) 6 , for all integers n ^ 1. Proof (by weak induction): Basis Step: P(n) is true for n = 1, for:1Σj...
There are 3 main types of mathematical proofs. These are direct proofs, proofs by contrapositive and contradiction, and proofs by induction. What is an example of proof in math? An example of a proof is for the theorem "Suppose that a, b, and n are whole numbers. If n does not divide...
destruct/induction assert rewrite setoid_rewrite(rewrite with binders) autorewrite rewrite_strat/autosetoid_rewrite intro/intros/revert/generalize/set/clear/clearbody refine/exact/assumption change/refine+ unification unify, roughly how an unuification algorithm can do its job by calling intantiate / ...