Practice Universality Of The Statement (18.1.3)

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9 questions

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6 sample questions

Question 1.
What is a subsequence?
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Think of sequences like (1, 3, 2). Which numbers can form a subsequence?
Question 2.
Define a strictly increasing sequence.
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Consider the sequence (a, b, c) — what should a be compared to b?
3Question 3.
What is a strictly increasing subsequence?
- Elements can be equal
- Each element is less than the previous
- Each element is greater than the previous
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Think of an example where this applies.
4Question 4.
True or False - Every sequence of 5 distinct real numbers contains a subsequence of length 5 that is either increasing or decreasing.
- True
- False
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Reflect on the definition of subsequences.
Question 5.
Prove the statement with a specific example of seven distinct real numbers.
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Arrange numbers visually to help identify patterns.
Question 6.
Demonstrate the pigeonhole principle clearly with 10 numbers and 3 distinct categories (such as odd, even).
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Digging into the counts will help clarify.

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