The Pigeonhole Principle espouses that if there are more objects than the places the objects are supposed to fit into, some of those places will have more than one object. For instance, if there are 20 pigeons and only 19 pigeonholes, one pigeonhole will have more than one pigeon.
If one hundred people in your neighbourhood leave between 7:30 and 8:00 A.M. and arrive 30 minutes later that means they will arrive between 8:00 and 8:30 A.M. This means that 100 people will have to arrive in 30 minutes.
We would have to fit 100 people in 30 minutes. The minutes are the pigeonholes and the people are the pigeons. There will therefore be a situation where at least 2 people will arrive at the same minute because there are many more people than minutes for them to arrive in.
A rational number is any number that can be repesented as a fraction. So every integer is also a rational number (because it can be written as a fraction with the denominator 1)
