1. The problem statement, all variables and given/known data Let m be a natural number. Find the flaw in the statement below. Explain why the statement is not valid, and change one symbol to correct it. "If T is a set of natural numbers such that 1) m [tex]\in[/tex] T and 2) n [tex]\in[/tex] T implies n+1 [tex]\in[/tex] T, then T = {n [tex]\in[/tex] N : n ≥ m} 2. Relevant equations Dunno. 3. The attempt at a solution Part 2) of the if statement tells us that T is an infinite set. I'm not sure exactly how 1) and 2) are connected. Hmmmm ... Help me get started.
Hmmm ... T is going to look something like {k, k+1, k+2, ...}, where k≥1 is an integer. That's basically what the second condition tells me. m is some element in T. That's all I know about m. Could m-1 be in T? As long as m>k.
Ok, so you don't know if m-1 is in T. On the other hand, m-1 is definitely NOT in [m,infinity). That suggests that T and [m,infinity) are not necessarily the same thing.