21 January, 2010

whoa

Ok, so I can't get to bed yet so I'll share this as it seemed to make quite a stir when I posted it as my status on facebook.

If I have an infinitely long sheet of paper and on the left side I start listing all of the natural numbers (positive integers: 1, 2, 3... etc) and then on the right side I write down all of the positive even numbers (2, 4, 6... etc). Which column will have more numbers?

I was listening to the show Uncommon Knowledge on my favorite NPR station (WGLT) when they were discussing this. It's not often that I get my mind blown but I'll say this was one time (another when I was a little kid and realised that what I see as green might be what you see as purple or grey and there's no way for us to compare). I highly recommend that if you're ever in Illinois in the Bloomington-Normal area you change your dial over to 89.1 FM for some great jazz and NPR programming during the week and blues (and Car Talk!) on the weekends.

4 comments:

Unknown said...

Can you please answer the question you have posed? My mind, she is being turned inside-out by it.

niftysunburn said...

That's the thing about it right?

If you write down all of the natural numbers and then all of the even numbers you can only write down one even number for every two natural numbers. Logic would tell you that there must be twice as many natural numbers as even numbers. The thing is though, that since both lists are infinite they will both continue on forever. That will effectively give both the same quantity of numbers (if one could quantify infinity that is).

Really, I prefer the answer that one of my friends gave me, "It's orange."

MJ said...

Isn't it fun when your mind is blown? Figuratively of course, in actuality it would be quite inconvenient. But anyhow, I also had that thought about the colors when I was a kid. It boggled my mind.

Becky said...

update. UPDATE!