14.1.6. Question Number 11

Try these first

1. 1.

   What is an irrational number?

   Hint

   Think about definitions involving fractions.

2. 2.

   Can you give an example of an irrational number?

   Hint

   Consider numbers that can't be precisely written as fraction.

3. 3.

   What is a key feature of irrational numbers?

   • They can be expressed as fractions.
   • They cannot be expressed as fractions.
   • They are always negative.

   Hint

   Consider their definitions closely.

4. 4.

   True or False: √2 can be expressed as a ratio of two integers.

   • True
   • False

   Hint

   Think about previous discussions regarding numbers.

5. 5.

   Prove using induction based on parity that the sum of any two odd integers is even.

   Hint

   Focus on the properties of odd integers.

6. 6.

   Using strong induction, show that if √n is irrational for n=2, it remains true for any integers beyond that.

   Hint

   Revisit the structure of your proof for clarity.