What is the flaw in the statement about T and how can it be corrected?

[Jamin2112]

Homework Statement

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 \in T and 2) n \in T implies n+1 \in T, then T = {n \in N : n ≥ m}

Homework Equations

Dunno.

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.

 

[Dick]

To get started think about this. Is m-1 in T?

 

[Jamin2112]

To get started think about this. Is m-1 in T?

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.

 

[Office_Shredder]

So is their equation for T correct?

 

[Dick]

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.