Let m be a natural number ...

  1. 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.
     
  2. jcsd
  3. Dick

    Dick 25,735
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    Homework Helper

    To get started think about this. Is m-1 in T?
     
  4. 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.
     
  5. Office_Shredder

    Office_Shredder 4,500
    Staff Emeritus
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    Gold Member

    So is their equation for T correct?
     
  6. Dick

    Dick 25,735
    Science Advisor
    Homework Helper

    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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