03/06/2011, 03:24 PM

3. 2 [n] 2 = 4

Proof:

2 [1] 2 = 2 + 2 = 4

Suppose 2 [n] 2 = 4 for a given n, then we wish to prove that 2 [n+1] 2 is also 4.

2 [n+1] 2 = 2 [n] (2 [n+1] 1) = 2 [n] 2 = 4

So it is proven by induction.

Proof:

2 [1] 2 = 2 + 2 = 4

Suppose 2 [n] 2 = 4 for a given n, then we wish to prove that 2 [n+1] 2 is also 4.

2 [n+1] 2 = 2 [n] (2 [n+1] 1) = 2 [n] 2 = 4

So it is proven by induction.