20 окт. 2014 г. · Regular induction requires a base case and an inductive step. When we increase to two variables, we still require a base case but now need two ...

31 июл. 2017 г. · Yes, you can indeed do induction on two or three or more variables at the same time ... no need to do one inside the other.

23 авг. 2018 г. · 1 Answer 1 · It is known that, for arbitrary x, if f(x,y) is true then f(x,y+1) is true. · Therefore for arbitrary x and all y, f(x,y) is true.

24 окт. 2010 г. · Here are some induction principles for two variables: P(0,0); ∀x,y.P(x,y)⇒P(x+1,y). ∀x,y.P(x,y)⇒P(x,y+1). ∀x,y.P(x,y). and. P(0,0); ∀x,y.

19 июл. 2013 г. · The induction hypothesis is that for all a and b, and a specific value of c, say k, we have the result. One then proves we have the same thing for all a, b, ...

16 июн. 2021 г. · As long as you prove enough "base cases", this is fine. If you like, think of it as doing the usual sort of induction on the sum, S=n+m.

23 февр. 2018 г. · The answer to the TLDR is yes. Often called "double-induction" or "nested-induction." See this question for several examples of double-induction in action.

11 мар. 2021 г. · Notice that I could have used two inequalities to reach the conclusion, one because of the induction step and another one because of 1+k>1.

29 янв. 2022 г. · A simple reason that induction works on n-ary formulae/predicates is that you can use iterated induction on unary formulae to derive induction ...

2 дек. 2018 г. · Not necessarily by double induction. You can prove ∀yP(n,y) by induction on y, with n whatever. If the proof works without any specific ...