3. (20 points) Every binary number (base 2) can be written as a natural number (base 10). The conversion uses the powers of 2. For example Base 2 0 Base 10 0 Conversion 1.21 + 0.2 - 2 1.21 + 1-20-3 1.22 + 0.21 + 0.20 - 4 1.22 0.21 + 1-20-5 1.22 + 1.21 + 0.20 - 6 1.22 + 1.21 + 1.20- 7 1.23 +0.22 + 0.21 + 0.28 10 3 4. 100 101 110 6 1000 8 1.23 + 0.22 + 0.21 + 1.2 9 1001 Consider the set of all binary strings, B = {x | x {0, 1}* and x starts with a 1 and the length of x = n for some n N}. B is countable and |B| INI. Give a bijection from B to N, so B is the domain 3. (20 points) Every binary number (base 2) can be written as a natural number (base 10). The conversion uses the powers of 2. For example Base 2 0 Base 10 0 Conversion 1.21 + 0.2 - 2 1.21 + 1-20-3 1.22 + 0.21 + 0.20 - 4 1.22 0.21 + 1-20-5 1.22 + 1.21 + 0.20 - 6 1.22 + 1.21 + 1.20- 7 1.23 +0.22 + 0.21 + 0.28 10 3 4. 100 101 110 6 1000 8 1.23 + 0.22 + 0.21 + 1.2 9 1001 Consider the set of all binary strings, B = {x | x {0, 1}* and x starts with a 1 and the length of x = n for some n N}. B is countable and |B| INI. Give a bijection from B to N, so B is the domain