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 Originally Posted by givememyleg
another dumb guy here, i think that's good analysis.
in a way it sounds like he's saying one set of infinity is larger than the other? but that sounds impossible, (infinity) = (infinity * 100) or whatever you want. infinity is even the same as infinity * infinity.
Some infinities are larger than others. They're considered to be different numbers. What's fun is that you can prove that some infinities are different from each other without being able to prove which one is larger.
The easiest place to start to wrap your head around it is getting an idea between what's countably infinite and uncountably infinite. The natural numbers {1, 2, 3....} are countably infinite, and all of the reals between 0 and 1 are uncountably infinite. You can prove that these two sets have different sizes with a little bit of logic. Without getting too deep into the math:
Step 1: Assume that they have the same size.
Step 2: Do some shit.
Step 3: You get a massive contradiction that proves the assumption in step 1 is false.
I'm pretty sure the details of step 2 are covered in first-level real analysis classes, though you might be able to find an easy-to-digest version online somewhere.
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