Trouble finding loop invariant for this while loop
Unfortunately, you can't prove partial correctness of your algorithm because it is incorrect.

EDIT: The algorithm provided is indeed correct.

Aditionally, you can't prove that an algorithm is "inductive". You can prove its correctness by using loop invariants,which are quite similar to mathematical inductions.

We must show three things about a loop invariant:

Initialization:

Before you start the loop,check if your initialization is correct. 

You want to check if there is an even number of positive numbers in your list A. You set up the variable i to equal 0, therefore your loop begins at the first index of your list. 

The variable even is set to True. If it were set to false, and you had 0 positive integers, it would return false, which is incorrect.
Therefore, initialization is correct.

You can see initialization as your base case.

Maintenance:

If your invariant holds from iteration to iteration.

The body of your while loop checks if an integer in index i of your array A is positive. If that condition is true, it sets the boolean variable "even" to "not even".

Since it flips the value of even equal to the amount of positive integers in your list,the maintenance is correct. 

Termination:

What happens when the loop is over?

The last step increments the variable i by 1. When the loop ends, i &lt; A.length, which is correct.

The algorithm will return either True or False based on the amount of positive integers. Since initialization and maintenance are correct, the algorithm is correct.