THIS INFINITY IS TOO SMALL – Marilyn Armstrong

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 out 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 back forever into the minuses as well and infinitely 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 others.

Finite and infinite sets. Two sets have the same cardinality when there is bijective function associating them. Cardinality it is reflexive, symmetric and transitive. Countable sets: the set of all integers, set of even numbers, positive rationals (Cantor diagonalization). Set of real numbers between 0 and 1 has same cardinality asset 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 to explode 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 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, 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. Retired! Yay!

17 thoughts on “THIS INFINITY IS TOO SMALL – Marilyn Armstrong”

  1. I thought I could make some money writing after I retired. Two books written. One was on kindle for a while. Thirteen copies sold to people I knew. I took it down. Finding a publisher who will pay me for it is harder than writing it.
    Still thinking about ways to add income but found nothing yet.

    I took one course in algebra in college. Barely made it through. I have infinite problems with the subject.

    I took philosophy. I remember one of the first assignments was to write an essay about a straight line. I never went on to another philosophy course.

    Pondering straight lines and solving advanced math. No, I went another direction.

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  2. My husband is numbers, I’m words. If I need “square the circle” or areas calculated, he does that. If he needs spelling checked, I do that.
    I looked at that infinite/finite series for about five minutes, and thought, okay…my husband glanced at it on his way out and said, yeah, so?
    I do love numbers, Fibonacci series, golden mean, factoring, primes, the magic of Nine. None of it especially useful, it’s like legos with numbers.

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    1. How ironic is it that I actually LIKED algebra. Not because it got me answers I wanted, but because it was a puzzle. Find “X” or “X+Y” or whatever. I got the wrong answer almost all the time, but I enjoyed — when it wasn’t a class and there was no pressure on me to come up with a right answer — the puzzle of it. But that is also why I don’t like turning writing into puzzle-solving. Writing for me is about the music of language, the flow of sound, the curve of the world in a word. When you start turning it into a game, that’s okay if I want to play scrabble or boggle … but it’s not writing.

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  3. I was never quite good enough with maths to wrap my head around Calculus and derivatives or the deeper mysteries of set theory and bijective functions!:-)

    I have however spent sleepless nights considering the infinity of infinities ‘large’ and ‘small’. 😉

    Knowing that there is a separate infinite set of numbers between 0 and 1 as there is between 1 and 2, and between 2 and 3, etc must mean that everything is infinite…. even your bank balance! Sadly this does not stop bank managers or store owners asking you for multiple ‘infinities’ of money. Surely one infinity is enough? Right?

    According to some cosmologists there are only actually 3 numbers: o, 1 and infinity. ( plus their opposites where the number plus it’s opposite cancel each other out to get 0 !) Infinity is simply 0 refracted through 1 (and vice versa). Everything else is simply combinations those modified by one of basically just 2 functions: addition or division (subtraction and multiplication being the comparable refractions through 1 of either adding or dividing). So everything you need to know about numbers is contained in: ‘plus or minus 1+0/infinity’. You might just need to apply that knowledge in all it’s possible combinations many, many times over to get a particular ‘result’. Simple. 😉

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  4. There are an infinite number of infinite sets out there. And multiplying infinity times infinity gives you the same infinite answer as if you just added infinity and infinity… or even infinity plus one.

    Math doesn’t make sense. This is why I stock shelves for a living…

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    1. There ARE people — I’ve met a few through the years — to whom math is another language and they understand it. I am not one of them. Neither is Garry. I’m better at simple arithmetic than he is, but that’s it.

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