# Let m be a natural number ...

by Jamin2112
Tags: natural, number
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 P: 920 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 $$\in$$ T and 2) n $$\in$$ T implies n+1 $$\in$$ T, then T = {n $$\in$$ 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.
 Sci Advisor HW Helper Thanks P: 25,235 To get started think about this. Is m-1 in T?
P: 920
 Quote by Dick 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.

 Emeritus Sci Advisor PF Gold P: 4,500 Let m be a natural number ... So is their equation for T correct?
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P: 25,235
 Quote by Jamin2112 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.

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