1. [10 marks] we begin with some mathematics regarding uncountability. let n = {0, 1, 2, 3, . .} denote the set of natural numbers. (a) [5 marks] prove that the set of binary numbers has the same size as n by giving a bijection between the binary numbers and n. (b) [5 marks] let b denote the set of all infinite sequences over the english alphabet. show that b is uncountable using a proof by diagonalization.

Self contained sequences of actions to be performed are? a. expressions b. algorithms c. functions d. formulas

The value of sin(x) (in radians) can be approximated by the alternating infinite series create a function (prob3_2) that takes inputs of a scalar angle measure (in radians) and the number of approximation terms, n, and estimates sin(x). do not use the sin function in your solution. you may use the factorial function. though this can be done without a loop (more efficiently), your program must use (at least) one. you may find the mod() function useful in solving the problem.

Which of the following is an example of a boolean condition that python could recognize? a: grade + 70 b: grade > = 70 c: "you should aim for at least a 70." d: "you have a 70."