One of the biggest questions posed in mathematics is: what is infinity. Infinity isn’t really a number; it’s more of a consensus that has been made inside the scientific establishment, in order to be able to solve problems that couldn’t be solved without the existence of the concept of infinity. For many of us infinity isn’t something that we necessarily feel we are in contact with, that it isn’t part of our day to day lives, but of course every computer, calculator, or any sort of machine that has to be programmed mathematically is based on the existence of infinity.

There are still some debates whether infinity exists or not. Everything boils down to whether or not there is such a thing as the biggest number. Infinity is a concept that suggests that there is no such biggest number, because we can always add one to that number and we will get a bigger number. Some mathematicians have suggested an alternative to this theory, by suggesting that there is a biggest number, and mathematics works like a cycle, in the sense that if you add one to this biggest number, you will come back to zero.

Of course this still leaves the problem of the biggest number. For a period of time, the biggest number used in mathematics was a googol. A googol is ten to the power of a hundred. Basically it is one followed by one hundred zeroes. This may not sound like such a big number but it is actually larger than the number of atoms in the universe. Later, the number googolplex was used in a mathematical formula. A googolplex is one to the power of a googol. This number is so large that there aren’t enough atoms in the universe to write each of the zeroes that the googolplex contains. This number was of great insight for a possible answer to the question what is infinity? Actually the biggest number to date ever used in a mathematical proof is the so called Graham’s number. This number is much bigger than a googolplex and the formula behind deducing it stands at core of tracking information over the internet. But if you look at thing at an infinite scale you will see that even Graham’s number is not actually closer to infinity than the number one. So the question remains: what is infinity?

Some of the proprieties of infinity can be summed up in a hypothetical situation devised in the nineteenth century by an English mathematician. This can shed light on what infinity really is. If you go to a hotel with an infinite number of rooms, which is fully booked, will you still find a room for yourself? Well, because there is no biggest number, than there is no last room. By this judgment, there will always be a next room to go to. So, if the guest from room one, moves to room two, and the guest from room to, moves to room three and so on, al the guests will move to the next room, and you can get room number. So, infinity plus one is infinity. What if you want to com to the hotel with an infinite number of your friends? Would you all have a place to stay? Well, if you think about it, you will find out that the list of all whole numbers is exactly the same length as the list of even numbers. This may sound odd but since they all contain an infinite number of numbers, you can start paring up the first number from one list with the first from the second list, the second number from the first list with the second number from the second list and so on. Since they both go on forever you will always find a pair for every number in the first list to every number in the second list. So, coming back to our problem, if every guest is moved into even numberd rooms, guest from room one, goes to room two, guest from room two is moved into room four, and so on, all the odd rooms, which there is an infinte off, are free, for you and all your friends. So, infinity plus infinity is infinity. The paradox with infinity is encountered when you subtract something from infinity. If an infinite number of guests left, than the number of guests remaining can be any number. If an infinite number of guests leave, and three remain, the infinity minus infinty is three, if four remain, tha the answer is four, so basically, and infinity minus infinity is whatever you like.

These are just some weird proprieties of infinity. They don’t definitively answer the question what is infinity, but they give us a glimpse into what it could be. I think that solving this mathematical dilemma, if it can be solved, may be one of the biggest scientific breakthroughs off all time.  Still, infinity eludes us, and it gets weirder and weirder, because as the german mathemathician Cantour has dicovered, some infinities are bigger than others, a theory which makes this question even more intriguing.

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