Wildlife Math Lesson

Many of us are familiar with the concept of infinity. To most of us, it may simply mean a number that goes on forever, or numbers that go on forever. But how do we prove that infinity is infinity?

David Hilbert gave a lecture in 1942 that offered a simple and interesting solution. He used a hotel to demonstrate that infinity+1 and infinity+infinity all still equal infinity.

Say we have a hotel called the Grand Hotel. This hotel has infinity rooms, and is capable of hosting infinity people. One day, a new tourist comes to live in the Grand Hotel. However, the hotel rooms are all occupied. The hotel manager Bob says anyway, "No problem, we can fit you in!" Bob tells all the current guests to move UP one room.

The guest in Room 1 moves to Room 2, The guest in Room 2 moves to Room 3... The guest in Room N moves to Room N+1. This way, the first room is empty and since there are infinity rooms, all the guests will still have a room. This is the concept of infinity+1=infinity. 

One day a bus pulls into the Grand Hotel's parking lot. The bus contains infinity people. When these infinity tourists ask for a room, manager Bob scratches his head for a couple of minutes, then says, "No problem, I can find you some empty rooms!" He tells all the current guests to move the the Room TWICE their current room number. 

The guest in Room 1 moves to Room 1x2=2, the guest in Room 2 moves to Room 4, The guest in Room 3 moves to Room 6, the guest in Room N moves to Room 2N. This way, all the current guests will be occupying the even number rooms.  Now the new infinity guests could move in to the odd numbered rooms. Since there are infinity odd and even numbers, the Grand Hotel can still accommodate every guest so far. This is the concept of infinity+infinity=infinity.

But what if infinity new tourists come labeled with all real numbers (decimals) between 0 and 0.5? (e.g. 0.31415..., 0.49112...) These decimal tourists ask Manager Bob for rooms. After scratching his head for a long time, Manager Bob finally says, "I'm sorry, we cannot find any rooms for you here. You'll have to try Hotel Uncountable around the corner." These decimals were another DIFFERENT group of infinity, not in the whole number group.

At this point, I realized that this "Uncountable Infinity" situation is parallel to our humans vs. animal competition today. We are the current guests/Manager Bob that are able to live in the Grand Hotel, but when the wild animals (infinite decimals) try their luck here, we kick them out and they cannot survive.
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The difference here is that there are not infinity animals and there are not infinity humans, either, if we continue to treat animals as if they are below us. In a way, humans and animals are all equal. We were all created by the same God or we all evolved from one single cell. True, lions cannot do trigonometry, but they can let their pride flow flood the lands and have their courageous roar be heard around the world. Animals, in a way, have helped us reach where we are in life today. Christopher Columbus sailed to the Americas on a ship. Why did he use a ship? Because it was faster and held more supplies. BUT, also so he wouldn't get eaten up by sharks and have to swim around in freak storms. Nature has shaped us, and though we don't know it, wildlife was there the whole entire way. They deserve the infinite amount of respect there is in the world.