this post was submitted on 12 Jul 2023
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Showerthoughts
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A "Showerthought" is a simple term used to describe the thoughts that pop into your head while you're doing everyday things like taking a shower, driving, or just daydreaming. The best ones are thoughts that many people can relate to and they find something funny or interesting in regular stuff.
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I mean, Cantor said so, not I. But an easy example
Imagine a list of all whole numbers. 1, 2, 3 on up and up. Obviously this list is infinite - numbers do not end.
Now imagine a list of all real numbers - that is, all numbers plus their decimal amounts between each while number. 1, 1.1, 1.11, 1.12, 2, 2.1, and so on. This list is also infinite - but it is also inherently larger than the infinite list of only whole numbers. It has more numbers.
That's like saying am infinite number of feathers is lighter than an infinite number of bricks. Neither is heavier than the other - they're both infinitely heavy.
You’re measuring a quality of the two objects, not the quantity, which might make a difference. I’m just sharing something I learned that I think is cool:)
It's an interesting concept, for sure, don't get me wrong. It's intuitive to see the scenario of "different infinities" as being different sizes and believe it makes sense, but it doesn't pan out. It's weird because infinity is used in regards to numbers, but it's not a number itself. It's more the antithesis of a number - it's everything. It's a tool we use to interact with the concept of something that specifically can't be measured. Measuring implies limits or bounds, but something that is endless has neither.
So saying there's an infinite number of this or that is more akin to the "riddle" of if 100lbs of feathers weighs less than 100lbs of bricks. The trick is they both weigh the same, even though our brain might not intuitively realize that, just like infinities. Ultimately, it'd be more accurate to say there's infinities within infinities, which is another tricky concept all on its own.