“That’s the idea!”
A short tale about chairs and even numbers.
Natural Numbers: 1 , 2 , 3 , 4 , 5 …...
Even Numbers: 2 , 4 , 6 , 8 , 10 …...
Some years ago, two schoolboys were putting out rows of chairs in the assembly hall. They both felt slightly hard done by as they were sure that they were given more jobs to do than the other pupils. Georg and Henri were bright pupils and they loved mathematics. Each was convinced that he was ever so slightly better than the other at algebra.
As Georg and Henri completed yet another row of chairs, Henri started to become slightly anxious.
“What’s the matter?” asked Georg.
“We need to know exactly how many pupils are coming for assembly and we have only ten minutes before they arrive. We will never be able to count them in time!” replied Henri.
“Don’t worry” said Georg with an infuriating air of calm. “We will fill twenty rows of chairs and then open the doors. If there are too few chairs, then we will see pupils standing. If there are too many chairs, we will see empty places. Either way we can solve the problem more quickly than counting all of the pupils in the school.”
Henri was unconvinced but he knew that Georg was a logical chap. Surely it would all be fine.
Soon enough, the school bell rang and the pupils began to file in to the hall. To Henri’s astonishment, they had laid out just five fewer chairs than required. This was soon rectified.
“You see - every pupil has a chair and every chair has a pupil. That shows that there are the same number of pupils as there are chairs.” said Georg triumphantly.
“Well, we still don’t know how many pupils there are!” protested Henri.
“It really doesn’t matter—we just needed to make sure that there were the same number of each.”
A the end of the assembly, Henri seemed dissatisfied but he grudgingly congratulated Georg on solving the problem. Before heading off to lessons, Henri asked: “How on earth did you come up with the idea?”
“Oh it’s easy once you know that the amount of even numbers is the same as the amount of natural numbers” Georg replied.
“Oh now you are just being silly.” said Henri “That’s the wildest idea you have ever come up with!”
They went their separate ways each content that they were correct regarding even numbers.
Of course the must be more natural numbers than even numbers.
Mustn’t there?