4. For each set determine whether the following sets are open, closed, or neither. If a set is not open, find a point in the set for which there is no E-neighborhood contained in the set. If a set is not closed, find a limit point'that is not contained in the set. (a) Q (b) N (c) {z ER:0}

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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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**Question 4: Set Openness and Closedness Analysis**

Determine whether the following sets are open, closed, or neither. If a set is not open, identify a point in the set for which there is no ε-neighborhood contained in the set. If a set is not closed, find a limit point that is not contained in the set. 

(a) **Q** (the set of rational numbers)

(b) **N** (the set of natural numbers)

(c) **{x ∈ ℝ : x ≠ 0}** (the set of all real numbers except zero)
Transcribed Image Text:**Question 4: Set Openness and Closedness Analysis** Determine whether the following sets are open, closed, or neither. If a set is not open, identify a point in the set for which there is no ε-neighborhood contained in the set. If a set is not closed, find a limit point that is not contained in the set. (a) **Q** (the set of rational numbers) (b) **N** (the set of natural numbers) (c) **{x ∈ ℝ : x ≠ 0}** (the set of all real numbers except zero)
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