How Can Infinity Come in Many Sizes? -- Quanta Magazine

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2. I studied this stuff when I was a math major 50+ years ago

Fascinating stuff.

BTW, the referenced article is well-written and accessible, I think. It only explains the first two levels of infinity, but that's enough to show that infinity is not one single entity. I'm not generally very impressed by scientific writing on the net--it's often written by journalists/writers who don't really understand what they're talking about. But these two writers both know their topic and can explain it clearly.