How about A equals the positive integers?
Define a subset A that is a subset the of Real Numbers that satisfies
1) 1 is an element of A
2) if n is an element of A then n+1 is an element of A
yet for which R sub >0 is not a subset of A.
I can't quite see how to
use induction in this problem, although I am fairly sure induction
should be used. Also I am confused as to how since it is given that 1
is in the set A then how can R sub >0 not be a subset of A?
If A is a subset of the reals then it can contain any positive or
negative number. We know 1 is an element of A....
Help would be appreciated!