学习笔记《Induction and Deduction》

归纳法(Induction,从个别到普遍,一级一级上台阶)和演绎法(Deduction,从普遍到个别,基于一个普遍的公理开始的推定)是最主要的两种逻辑判断方式,数学里面用的是 Induction,Deduction 则无法在数学推导中被使用的,因为数学推导不相信 Deduction(但是数学的基础是 Deduction)

Mathematical induction proves that we can climb as high as we like on a ladder, by proving that we can climb onto the bottom rung (the basis) and that from each rung we can climb up to the next one (the step).

除了归纳和演绎,还有一种叫做例证法:
http://mp.weixin.qq.com/s/0KvEPVmc3RhzFh9TiWpHjQ

课程地址:
https://www.youtube.com/watch?v=0UgID8C9RvE

Induction

Stong Induction

Deduction

是演绎法让数学归纳法变的有效(比如某些数学证明,归纳法是因为对自然数的演绎前提下,才是有效的):