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


    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 25,913
    Science Advisor
    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 4,487
    Staff Emeritus
    Science Advisor
    Gold Member

    So is their equation for T correct?
  6. Dick

    Dick 25,913
    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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