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Let m be a natural number ...

by Jamin2112
Tags: natural, number
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Jamin2112
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Jul16-10, 04:01 PM
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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.
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Dick
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Jul16-10, 04:05 PM
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To get started think about this. Is m-1 in T?
Jamin2112
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Jul16-10, 04:55 PM
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Quote Quote by Dick View Post
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
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Jul16-10, 05:01 PM
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Let m be a natural number ...

So is their equation for T correct?
Dick
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Jul16-10, 05:11 PM
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Quote Quote by Jamin2112 View Post
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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