Algorithms The definition for an algorithm is a finite set of instructions which, if followed, accomplishes a particular task. In addition, every algorithm must satisfy the following criteria: input: there are zero or more quantities which are externally supplied; output: at least one quantity is produced; definiteness: each instruction must be clear and unambiguous; finiteness: if we trace out the instructions of an algorithm, then for all cases the algorithm will terminate after a finite number of steps; effectiveness: every instruction must be sufficiently basic that it can, in principle, be carried out by a person using only pencil and paper. It is not enough that each operation be definite as in (iii), but it must also be feasible. Given the above definition for an algorithm, consider the two statements: a. Is n=2 the largest value of n for which there exists positive integers x, y, z such that xn + yn = zn has a solution? and b. Store 5 divided by zero into X and go to statement 10. Both statements do not satisfy one of the five criteria of an algorithm. Which criteria does each one violate?

Question

Algorithms

The definition for an algorithm is a finite set of instructions which, if followed, accomplishes a particular task. In addition, every algorithm must satisfy the following criteria:

input: there are zero or more quantities which are externally supplied;
output: at least one quantity is produced;
definiteness: each instruction must be clear and unambiguous;
finiteness: if we trace out the instructions of an algorithm, then for all cases the algorithm will terminate after a finite number of steps;
effectiveness: every instruction must be sufficiently basic that it can, in principle, be carried out by a person using only pencil and paper. It is not enough that each operation be definite as in (iii), but it must also be feasible.

Given the above definition for an algorithm, consider the two statements:

a. Is n=2 the largest value of n for which there exists positive integers x, y, z such that xⁿ + yⁿ = zⁿ has a solution?

and

b. Store 5 divided by zero into X and go to statement 10.

Both statements do not satisfy one of the five criteria of an algorithm. Which criteria does each one violate?