There are infinitely many real numbers between 0 and 1. Are there twice as many between 0 and 2, or are the two amounts equal?

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I know the actual technical answer. I’m looking for a witty parallel that has a low chance of triggering an infinite “why?” procedure in a child.

In: 1335

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Anonymous 0 Comments

Lets play the paper infinity game.

I have a sheet of paper, you have two sheets of paper. You have twice as many as me. I cut one page in half, you do the same. Now you have 3 sheets and I have 2. Now I cut a sheet in half and you do the same. I have 3 sheets and you have 4. You can do this forever, even though you started with twice as many sheets as me, you can only ever have one more sheet than me. After an infinite number of cuts, we both have an infinite number of sheets of paper, you are just 1 piece ahead of me. I can always catch up by making another cut though.

Another fun part of that, my pages get smaller a LOT faster than yours. You have double the “area” of paper as me to start. My first cut makes each sheet half the size, you require 2 cuts to do the same thing. By 3 cuts my paper is all 1/4th the size of where we started, it would take you 6 cuts to be in the same place as me. For me to get to 1/8th size I need 7 cuts, you need 14. You can always, eventually, get to the same size sheet of paper as me but it will always take you twice as many cuts to get there.

So, going one way you always only ever have one more page than me, going the other way you always take twice as long to get to the same page size as me. Either way we can both eventually get to where the other is, it just takes more work for one of us depending on what your end goal is.

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