# A Loveletter to Infinity

Birgit Schillinger – 2020 Teddy Rocks Maths Essay Competition Honourable Mention

Dear Infinity,

I must confess: I love you.

Haven’t seen you for a long time. Since I have known you, I have never forgotten your almost indescribable appearance. It is difficult to see you in total, but this makes you even more interesting. (Even? Sorry, I know you have more than an even side.) You are able to reach far out of my view.

Naturally, we both like to spend our free time outdoors. Walking – not necessarily hand in hand. Why not? Well, I feel so small compared to you. I am just a single. On the one hand if I join you forever, we will both add up to: you. I will have disappeared! On the other hand if I leave you, you will not notice that. It will not bother you at all: You just remain yourself.

You are admirable. So many people need a diet, but you can eat almost everything: all the finite stuff – and you just stay the same size. Overweight is – almost – no problem for you. And by a unit-fraction-trick you can make yourself so skinny, that you fit in a little piece of a line. It is so easy to change from tall to small by the reciprocal. But please don’t do this to the limit – this would end up in anorexia.

At Christmas you drove my sister crazy: She started to decorate the Christmas tree one hour before the guests arrived. She hung up two Christmas baubles on the tree, but you took off one of them. Half an hour later again: She hung up two Christmas baubles, you took off one of them. A quarter hour, an eighth and so on she repeated the same procedure: She hung up two, you picked one. Which baubles were hanging when the guests arrived? None! And then we then changed the procedure: My sister hung up again two Christmas baubles and you took away the odd Christmas baubles. Thus the even baubles were still hanging. So many!

We have the most fun when we go on holidays. I will never forget our last trip. After a wonderful day outside in nature we were looking for a hotel. Do you remember our trouble in David’s hotel called “Hilly’s Best”? It was booked out when we arrived. One of your relatives had already been there. But since your uncle David likes you very much, he found a magic way to offer us enough rooms (To find a room for me was the easiest problem, he said).

And just when we began to unpack our luggage, it became very loud outside: There was an endless queue of buses with your relatives who wanted rooms too. David gave us a rule in which rooms we had to move. There was quite a bit of calculation necessary. How I hated these long, long, never ending halls till I got to my new room!

At least you didn’t get lost. I worried I would never see you again. The next morning I was so happy to meet you in the breakfast room. You wore clothes with an impressive design (Later I found out that your friend Cantor designed these especially for you). They were all over with nice diagonals, densely printed. The beautiful zigzag made you look smaller than you are.

When I greeted you “You look great!”, a mathematician, who sat next to our table, interrupted us: “No, you are not at all great!” Usually I know you are very rational but this time you got very angry and changed your colour. You murmured some spells. I understood only something about “continuum”. And you asked Z, F and C (who are these boys? No, no, I am not jealous…) whether it was okay for you to summon your subsets. And they all came! Really, all of them! Then you changed your appearance and said: “Now, I am really big. Look at me.” Usually I can count on you. But this time I had no choice but to feel uncomfortable. I am not superstitious and what did you do? You magically changed your set-ting as if we were in Hogwarts. Can I still rely on you? I was confused. Your zigzag danced in front of my eyes. There were more than the diagonals now. Do all the subsets belong to your new outlook?  Or – I am not sure – is there something in between? Something unfamiliar and unidentified? That is what I definitely wish to know.

After breakfast you decided that the hotel does not meet your demand anymore. Therefore we left and you wished to relax on a field. We looked around. What did you mean, when you uttered: “I feel a bit lost.”? The situation became more and more complex but we found a place for a nice picnic in a plain plane. As soon as we settled down, good old Charly Freddy Gauss came along the way. And he introduced me to your brother who just came the other way and we all met near the corner “The Crossing Origin”. I would never have thought that it was your brother. He looked really (?) different from you. We talked about food and he told us that he is vegan now. Therefore, he planted in his fields all kinds of root vegetables. For every recipe he can find a root out there which fits exactly. And not only one. He let us try some roots. We had never tasted anything like this. Quite a new flavour I could not imagine before. Strange brother. I forgot his name but it was only one letter. He always spoke about himself, every sentence started with “I”. First I thought he is very self centred. But then we realised that he is extremely helpful. For almost every problem – he had a solution!

What a family!

I miss you. Let us meet soon again. Where? When? More Questions? Ask me.