# Let m be a natural number

## 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}

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.

## Answers and Replies

Dick
Science Advisor
Homework Helper
To get started think about this. Is m-1 in T?

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
Staff Emeritus
Science Advisor
Gold Member
So is their equation for T correct?

Dick
Science Advisor
Homework Helper
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.