How should I understand the definition of computational problem?
A computational problem is a mathematical object representing a collection of questions that computers might be able to solve. For example, the problem of factoring
"Given a positive integer n, find a nontrivial prime factor of n."
What is the mathematical object in the example above? Quoting Wikipedia again:
Commonly encountered mathematical objects include numbers, permutations, partitions, matrices, sets, functions, and relations.
So how can you 'represent' a collection of questions with numbers or permutations, matrices etc.? What is meant here is probably the following collection of sentences:
'find a nontrivial prime factor of 1', 'find a nontrivial prime factor of 2' and so on...
But the thing is - these sentences are not mathematical objects.
A little further in the article it reads:
A computational problem can be viewed as an infinite collection of instances together with a solution for every instance.
which makes perfect sense, but I don't quite see the relationship with the first definition.