Studying for an exam.... Please help me find the interior points, exterior points, and boundary points for these sets..... Only the 1st column (a-k) Thank you so much!

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Studying for an exam.... Please help me find the interior points, exterior points, and boundary points for these sets.....

Only the 1st column (a-k)

Thank you so much!

The image contains a list of set notations, labeled (a) to (l), which could represent various types of numbers or intervals. Here's a transcription of each:

(a) \( (3,5) \cup \{6\} \)

(b) \( (-\infty, 0) \cup (0,1) \)

(c) \{1, 2, 3, 4, 5, 6, 7, 8, 9\}

(d) \( (-\infty, 0) \cup [0,1) \)

(e) \(\mathbb{Z}\) (the set of all integers)

(f) \( (-\infty, 0) \cup (0,1] \)

(g) \( (-\infty, 0) \cup [0,1] \)

(h) \( \mathbb{R} - \{1, 2, 3\} \) (the set of all real numbers excluding 1, 2, and 3)

(i) \(\left\{\frac{1}{n} : n \in \mathbb{N}\right\}\) (the set of all reciprocals of natural numbers)

(j) \(\left\{\frac{1}{n} : n \in \mathbb{N}\right\} \cup \{0\}\)

(k) \(\mathbb{Q}\) (the set of all rational numbers)

(l) \(\mathbb{Q} \cap (0,1)\) (the set of all rational numbers between 0 and 1)

These set notations demonstrate different collections or intervals within mathematical contexts.
Transcribed Image Text:The image contains a list of set notations, labeled (a) to (l), which could represent various types of numbers or intervals. Here's a transcription of each: (a) \( (3,5) \cup \{6\} \) (b) \( (-\infty, 0) \cup (0,1) \) (c) \{1, 2, 3, 4, 5, 6, 7, 8, 9\} (d) \( (-\infty, 0) \cup [0,1) \) (e) \(\mathbb{Z}\) (the set of all integers) (f) \( (-\infty, 0) \cup (0,1] \) (g) \( (-\infty, 0) \cup [0,1] \) (h) \( \mathbb{R} - \{1, 2, 3\} \) (the set of all real numbers excluding 1, 2, and 3) (i) \(\left\{\frac{1}{n} : n \in \mathbb{N}\right\}\) (the set of all reciprocals of natural numbers) (j) \(\left\{\frac{1}{n} : n \in \mathbb{N}\right\} \cup \{0\}\) (k) \(\mathbb{Q}\) (the set of all rational numbers) (l) \(\mathbb{Q} \cap (0,1)\) (the set of all rational numbers between 0 and 1) These set notations demonstrate different collections or intervals within mathematical contexts.
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