Understanding what Infinity means was one of the fun things in my Mathematics education.

The first time I started to really understand it was after a Professor gave our class an example in a first year algebra course:

Suppose you have a hotel with infinite rooms, and every room is occupied, what do you do if someone shows up and wants a room?

Tell everyone to move 1 room down, and give the first room to the new guest.

Trust me that is a good answer to that question, but it also allows me to talk about the **Fallacy of Infinite income**.

When you are 20, 30 and sometimes even when you are forty, you feel that you will be earning income long enough to make all of your goals (financially), however, your potential to earn income is not infinite, and in fact it is quite finite (and countable, to use another mathematical term).

Countable? Think of it this way, if you assume you are being paid twice a month and you start working at age 24 and you retire at age 65 the number of pay cheques you have is:

Total # Pay cheques = 24 * (65-24) = 24 * 41 = **984 pay cheques**

Certainly not infinite, and a quite optimistic number, because this assumes you work all the way to 65 (or that you can work all the way to 65). What might cause less pay cheques?

All of these will reduce the number of potential pay cheques in your career, but even worse is not having a pay cheque number in mind by when you reach your financial goals.

- By pay cheque 864 being out of debt
- Pay off the house by pay cheque 900
- etc., etc.,

## I Won’t Have Infinite Income ?

The concept of infinite and income do not belong in the same phrase.

I’m putting my math geek hat on now…countable doesn’t imply finite. A set of things is countable if you can match them up 1 to 1 with the counting numbers (1,2,3,…). To be countable you just have to find a way to match things up, you don’t have to actually finish counting. This is interesting to mathematicians because there are infinite sets that are countable (integers, rational numbers) and others that are not (real numbers for example).