Infinite Bike

You may have just cycled into the Twilight Zone. Consider, for a second, a hypothetical bike rack with countably infinitely many slots for bikes, all of which are occupied – that is to say every slot has a bike. Is it possible that such a rack would fit on our planet. Let’s just say it does. One might be tempted to think that the bike rack would not be able to accommodate any newly arriving cyclists, as would be the case with a finite number of slots. If there are already an infinite number of cyclists parked at this bike rack are there anymore cyclists left to arrive? Afterall, is there anything bigger than infinity? Let’s suppose a new cyclist arrives and wishes to park their bike in our bike rack. Because the bike rack has infinitely many slots, we can move the bike occupying slot 1 to slot 2, the bike occupying slot 2 to slot 3 and so on, and fit the new bike into slot 1. By repeating this procedure, it is possible to make room for any finite number of new bikes. I wonder where all of these cyclists are going? Is your bike already in this rack? I wonder if mine is? Probably not because I’ll be out riding mine! I guess it all depends on what attracted an infinite number of cyclists to this place to begin with. Hmmmm!

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