T* is a recursive definition, a subset of the family of ternary strings. Let T* be the smallest set such that:
BASIS: 0 is in T*
INDUCTION STEP: If x,y in T*, then so are x0y, 1x2 and 2 x1.
a) Prove that if k in N, then there is no string in T* with exactly 3^k +1 zeros.
b) Prove that if...
I have got Q2 (sort of...) but am at a loss for Q1 since I am unfamiliar with the Well-ordering principle. I do not have to prove uniqueness of r and q though (I think).
Please help me out!
Q1
m, n are natural numbers (which include zero for the sake of this question) and n =/= 0, then there are natural numbers q and r such that m= qn + r and r < n. Use the Well-Ordering Principle to prove this fact.
Q2
There are 51 students in a class. Prove there are...