UC知道induction prove```
来源：百度知道 编辑：UC知道 时间：2024/05/21 10:29:51
Here's a really simple language we'll call P(for parentheses):
1. Atoms: λ in P.
2. More generally, if u is in P, so is (u).
In other words,P is the set of all strings over the alphabet{(,)}in which parentheses are paired.
Use induction to prove that,for every expression in P,the number of left parentheses is equal to the number of right parentheses.
可以稍微详细的写几个步骤吗，我可以加分的
1. Atoms: λ in P.
2. More generally, if u is in P, so is (u).
In other words,P is the set of all strings over the alphabet{(,)}in which parentheses are paired.
Use induction to prove that,for every expression in P,the number of left parentheses is equal to the number of right parentheses.
可以稍微详细的写几个步骤吗，我可以加分的
对于P中一个元素u，定义k（u）为左括号数-右括号数
More generally, if u is in P, so is (u).
则对任何u，k（u）=0，
所以the number of left parentheses is equal to the number of right parentheses.
详细点，大概就是这样的
首先
对于Atoms: λ in P. so k（λ ）=0-0=0
假设对于u in P 有 k（u）=0
则对于（u）
k（（u））=k（u）+1-1=k（u）=0
用数学归纳法就知道所有P中的元素，都有k（u）=0
其实我也不一定保证就是对的，只是我是这样认为的。
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