Final answer:
To prove that two distinct integers don't necessarily have a third integer between them, one can use the concept of consecutive integers. For example, 3 and 4 are distinct but have no integer between them, while 3 and 5 do have an integer between them, which is 4.
Step-by-step explanation:
The question 'proving that 2 distinct integers does not mean there will be a distinct third integer between them' explores a concept in number theory, a branch of pure mathematics. Two distinct integers, say 'a' and 'b', where a < b could have an integer between them if the difference b - a > 1. If b - a = 1, then they are consecutive integers with no integer in between.
For instance, take the integers 3 and 4. They are distinct integers, but there is no other integer that lies between them because they are consecutive. In contrast, for the integers 3 and 5, there is a distinct third integer between them, which is 4. The concept that there must be a integer between any two distinct integers is a common misconception corrected by understanding that consecutive integers are exceptions to this.