College was not, as it turned out, particularly useful for practical stuff. Although I learned a reasonable amount, it had a tendency to be the kind of thing that makes great conversation while playing Trivial Pursuit rather than  while trying to figure our your household budget for the month.

Consider the subject of infinite sets. I am not a mathematician. I’m okay with arithmetic and I can figure out a basic, algebraic equation if you give me enough time and scratch paper … but otherwise? Unless it’s part of a computer language, I’m at a loss.

Finite versus infinite sets. Equipotent sets. Countable sets. Example!

I remember infinite sets because it was similar to trying to understand time travel.

An infinite set is any combination of numbers that has not end. There are lots and lots of them. All positive numbers, like: 1,2,3,4,5,6,7 … and obviously, you can keep counting until the moon turns blue and the world is exhausted.

But what about an infinite set of all negative AND positive numbers, so that they go backward forever into the minuses as well and forward into the positives. Forever and a day. With no end. That would be twice as big as all positive number … but equally infinite.

There can be infinite sets of only numbers which divide by three or cardinal number and any bizarre combination of fractions. They are all infinite, but some are bigger than other.

Finite and infinite sets. Two sets have the same cardinality when there is bijective function associating them. Cardinality is is reflexive, symmetric and transitive. Countable sets: set of all integers, set of even numbers, positive rationals (Cantor diagonalization) Set of real numbers between 0 and 1 has same cardinality as set of all reals. Computability of functions.

How can one infinity be bigger than another infinity? Apparently universes are sort of like that and now, my brain is due for explosion because I can’t keep this kind of information in there.

Our personal numeric world consists of shockingly finite numbers. That’s one of the amazing parts of retirement. You have what you have and you will never have more, unless you hit the lottery or have an extremely rich relative planning to die and leave his fortune behind for you. Retirement income just “IS.” It won’t get bigger. Retirement income pretty much stays the same while the world trundles on. Life and the universe may be infinite, sort of, but retirement income is not.

It’s just a thought to ponder. If you feel like pondering.

Author: Marilyn Armstrong

Writer, photography, blogger. Previously, technical writer. I am retired and delighted to be so. May I live long and write frequently.


  1. I don’t know if I could do it today. I remember chasing x and y all over the place with all their ups and downs. I could even do logarithms and antilogarithms, but you had to have the book. Since the invention of the pocket calculators who needs logarithms. I wonder if they still print the books. Oh, the days when I had a brain and not a rusty piece of body work.

    Liked by 1 person

    1. I know people who were physicists who look at books they WROTE and can’t remember what they were thinking. I can’t remember 1/4 of what I used to know. If it weren’t for Google, I wouldn’t even remember the 1/4 of it all. Use it or lose it. I’ve lost it.

      Liked by 2 people

  2. One of my students from Brazil said his physics teacher explained infinity by starting a line on the blackboard, continuing it all around the room to the door, walking out and not coming back for a week (and not continuing the line. “See?” he said, “That line is still going.” I think that’s pretty cool. I’m sure the students uncertainty made them get a visceral understanding of the idea.

    Liked by 2 people

    1. It’s a great idea and rather mind boggling. The idea of multi size infinities went into that strange hole where I keep trips in time and flying at warp speed. It’s weird how easily I absorb broad concepts like this, but can’t do a simple set of numbers without making dozens of mistakes. I think I’m the person for whom they invented calculators.


      1. So much is done by computer now, but you certainly want someone to be able to do this, should the need arise. Who knows what’s going to happen next.


  3. You lost me at ‘Equipotent sets’ ! 😉

    I like contemplating this stuff but as you said – our human brains are not really all that well equipped to understand the concept of infinity(s) – we have nothing we can really ‘hang’ it on!

    While i agree that retirement income certainly is not infinite – we would not want or need it to be since we only have a few short finite years in which we can spend it before… well, you know.

    I strongly disagree though that it has to be limited to less than or equal to what you are getting currently. There are almost an infinite number of ways you could increase it if you put your mind to it! The internet is opening up millions of opportunities – some of them even legal! 😉

    Go Spike! (and Garry the Samoan!)



  4. The complicated math and physics I had to learn (and basically failed at doing that) was what soured my on my love of meteorology when I was in college. I’m glad there are people who understand this kind of stuff and whatever practical implications it may have, though. I can picture a couple of mathematicians bragging over whose infinity is bigger…


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