The Infinite Income Fallacy

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 achieve 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 Chques = 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?

  • You decide to retire before 65
  • You are disabled before 65
  • You get laid off a few times

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 chque 900
  • etc., etc.,

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


{ 7 comments… add one }

  • Greg September 18, 2013, 2:18 PM

    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).

    • bigcajunman September 18, 2013, 2:26 PM

      I stand corrected, yes, countable still can be finite, what is interesting is tehre are INFINITE real numbers in between the integers 1 and 2 (mind blowing fun of math).

      • Greg September 18, 2013, 2:43 PM

        What’s even more interesting is there are *more* real numbers between 1 and 2 (or even any pair of rational numbers no matter how close they are) than there are integers. The rational numbers, like the integers, are countable, there is the same infinity of both of them. The size of the set of real numbers is a different kind of infinity- the uncountable kind.

        • bigcajunman September 18, 2013, 5:44 PM

          Ain’t mathematics mind blowing? How can someone say it isn’t just THAT cool!!! (no I am not being sarcastic, I am being serious)

  • September 18, 2013, 10:16 AM

    But, if you take your income and invest it in something – you really can approach a scenario where you get much closer to infinite income. Remember, working a job with a paycheck is just one way to produce income :-)

  • September 18, 2013, 7:14 AM

    Wait, What? I was told a career in sales had unlimited earning potential. Now you’re telling me there’s a cap?

    • Denis September 19, 2013, 1:28 PM

      Yup there is a cap! As per your account name Life Insurance Canada, when you have sold life insurance to every person in the world, you are maxed out, assuming that the birth and death rates are equal, that when you lose one you gain one. And I agree! Math IS mind-blowing.

      My own total income from life insurance sales is $0.00, so better luck than mine with that.


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