this post was submitted on 06 Jan 2024
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I considered deleting the post, but this seems more cowardly than just admitting I was wrong. But TIL something!

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[โ€“] deo@lemmy.dbzer0.com 1 points 10 months ago (1 children)

It's like arguing that a kilogram of feathers weighs less than a kilogram of bowling balls because the scale goes up less for every feather I put on the scale compared to every bowling ball I put on the scale.

I'm arguing that infinity bowling balls weighs more than infinity feathers, though

[โ€“] Breve@pawb.social 2 points 10 months ago* (last edited 10 months ago)

Try thinking of it like this: If I have an infinite amount of feathers, I can balance a scale that has any number of bowling balls on it. Even if there was an infinite number of bowling balls on the other side, I could still balance it because I also have infinite feathers that I can keep adding until it balances. I don't need MORE than infinite feathers just because there's infinite bowling balls. In the same way if my scale had every rational number on one side I could add enough even numbers to the other side to make it balance, but if I had all the irrational numbers on one side of the scale then I would never have enough rational numbers to make it balance out even though they are also infinite.

Edit: I suppose the easiest explaination is that it's already paradoxical to even talk about having an infinite number of objects in reality just like it would be paradoxical to talk about having a negative number of objects. Which weighs more, -5 feathers that weigh 1 gram each or -5 bowling balls that weigh 7000 grams each? Math tells us in this case that the feathers now weigh more than the bowling balls even though we have the same amount of each and each bowling ball weighs more than each feather. In reality we can't have less than zero of either.