Okay, so I’ve been messing around with some numbers lately, and I stumbled upon something that I thought was pretty cool. I wanted to share my little experiment with you guys, it’s nothing fancy, just playing around with some basic math stuff, you know?
So, I started with these two numbers, 169 and 81. Don’t ask me why I picked these two, they just popped into my head. I was curious about what I could do with them. First off, I tried to see if there was a simple way to break them down. Like, could I simplify the fraction 169/81? Turns out, it’s already in its simplest form. But I did see that it’s about 2.086 in decimal form, which I thought was neat.
Then I got into this whole thing about sets. You know, like in math class when they talk about sets and subsets? Yeah, that stuff. I imagined 169 as the total number of things in a big group (they call it the universal set, or U). Then, I thought of 81 as the number of things in one smaller group (let’s call it set A). I was just messing around, seeing what other numbers I could come up with.
- I thought, what if there’s another group, set B, with, say, 66 things?
- Then I started wondering, what if 47 things are in both set A and set B? That’s like the intersection, right? So, I figured out that if 47 things are shared, then there must be 81 + 66 – 47 = 100 things in total in either set A or set B or both. I think they call that the union. I wrote it down as: if n(A∩B)=47, then n(A∪B) = 100.
But then I took a turn. What if I knew the total number of things in either set A or set B (the union) was, let’s say, 147? Could I figure out how many things were shared between the two sets? So, I did some more number crunching and figured that if n(A∪B)=147, then the number of shared things, n(A∩B), must be 81 + 66 – 147 = 0. That makes sense, right?
I spent a good chunk of my day just playing around with these numbers, flipping them around, and seeing what I could come up with. I even tried looking up some stuff online. Mostly just random articles and videos about math things. It was kind of a rabbit hole, to be honest. I kept finding more and more questions to ask myself.
I know it’s not groundbreaking stuff, but I had fun with it. It was like a little puzzle to keep my mind busy. It made me think about all those math concepts I learned way back when, and how they can be applied to simple things. I think this is really fun and I did some calculations like those. I felt great about it and I’d like to try other number sets.
