Computational problem - definition 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.
But the thing is - these sentences are not mathematical objects.

Yes, they are. A set of sentences can be a mathematical object. Just about anything can be a mathematical object.


A computational problem can be viewed as an infinite collection of instances together with a solution for every instance.

[...] but I don't quite see the relationship with the first definition

Well, &quot;an infinite collection of instances together with a solution for every instance&quot; is a mathematical object (representing a collection of questions that computers might be able to solve).