# WHEN ONE INFINITY IS BIGGER THAN THE OTHER – 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 no 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 they go back forever into the minuses as well and forward into the positives. Forever and a day. Without 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 is reflexive, symmetric and transitive. Countable sets: a set of all integers, set of even numbers, positive rationals (Cantor diagonalization) Set of real numbers between 0 and 1 has the same cardinality as a 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 an explosion because I can’t keep this kind of information 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, but retirement is not.

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

Categories: Humor, knowledge, learning, mathematics

### 12 replies

1. How often have you made use of that fancy math? …me neither…..I guess they were trying to get us to think or give up?
Leslie

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2. Fixed incomes are infinitely disturbing and disheartening.

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3. I’m with Sadje. But retirement income is kicking us in the buttocks!!

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4. I did a little algebra in high school but that was way over my head. I did quite like algebra as a puzzle-solving exercise but I never figured out what I would ever use it for in everyday life. Fixed incomes, however, I understand only too well.

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5. Memories af school and those mysterious decimal points that had unendless numbers

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• Pi, the number which never ends.

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6. Um. Had to skim this one, Marilyn. It was making me dizzy.

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• Think time travel and parallel universes. Then take a long nap.

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• I think I’ll take the nap first.

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7. So true. The first part of the post was way over my head but I got the later part. 🤪

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• It’s just like time travel. How can one infinity be bigger than another? Aren’t all infinities the same size? No, they aren’t.

But retirement is easy. They send you too little money and you do your best to live on it.

Liked by 1 person

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