18.1.5. Contradiction and Conclusion

Try these first

1. 1.

   Define a strictly increasing sequence.

   Hint

   Think about a ladder.

2. 2.

   What does a subsequence mean?

   Hint

   It's like taking steps, skipping some.

3. 3.

   What type of sequence has all numbers increasing?

   • Strictly Decreasing
   • Strictly Increasing
   • Non-Strict

   Hint

   Consider the sequence like stairs going up.

4. 4.

   True or False: A subsequence can skip elements.

   • True
   • False

   Hint

   Think about selecting without restricting proximity.

5. 5.

   Given a sequence of 10 random integers, prove that there exists a strictly increasing or decreasing subsequence with length 5.

   Hint

   Break down the numbers into subsequences and analyze their lengths.

6. 6.

   Create a sequence of 12 distinct numbers and identify an increasing or decreasing subsequence of at least 7 numbers.

   Hint

   Try ascending and descending order to guide your selection.