# Math Help - Induction Set Proof

1. ## Induction Set Proof

Prove the following theorem

If G is a collection of induction sets, then the intersection of all the sets in G is an induction set.

2. Originally Posted by noles2188
Prove the following theorem

If G is a collection of induction sets, then the intersection of all the sets in G is an induction set.

Since all $G_i$ are all inductive $1\in G_{1}\wedge 1\in G_{2}\wedge 1\in G_{3}$ and............................................ $1\in G_{n}$ =====> $1\in\bigcap G_i$.

Suppose now $k\in\bigcap G_i$ ====> $k\in G_{1}\wedge k\in G_{2}\wedge k\in G_{3}$ and........................................... $k\in G_{n}$====> $k+1\in G_{1}\wedge k+1\in G_{2}\wedge k+1\in G_{3}$ and............................................... .. $k+1\in G_{n}$=====> $k+1\in\bigcap G_i$

Hence $\bigcap G_i$ is inductive