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Verifying some definitions

  1. Dec 10, 2012 #1

    Zondrina

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    Just a few definitions I would like to verify so I'm not studying the wrong stuff.

    Interior Point : A point [itex]Q \in S \subseteq ℝ^n[/itex] is an interior point of S if [itex]\forall \delta > 0, \exists N_{\delta}(Q) \subseteq S[/itex]. The interior of S consists of all interior points and is denoted [itex]S˚[/itex]

    Boundary Point : A point [itex]Q \in S \subseteq ℝ^n[/itex] is a boundary point of S if [itex]\forall \delta > 0, \exists P_1 \in S \wedge P_2 \in (ℝ^n - S) \space| \space P_1, P_2 \in N_{\delta}(Q)[/itex]

    Limit Point : A point [itex]Q \in S \subseteq ℝ^n[/itex] is a limit point of S if [itex]\forall \delta > 0, \exists P \in S \space | \space P \in N_{\delta}(Q), \space P≠Q[/itex]

    Trying to condense my stuff, hopefully I'm doing this correctly.
     
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  3. Dec 10, 2012 #2

    micromass

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    It should be [itex]\exists \delta >0[/itex].

    OK. But these definitions also hold if you don't demand [itex]Q\in S[/itex].
     
  4. Dec 10, 2012 #3

    Zondrina

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    I thought that it was for all deltas I choose? What if I chose delta so large that my neighborhood was contained in the compliment?

    Also, for the purposes of a calc II course, we're assuming Q is inside of the set, so I should be good there for now.
     
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