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PHILOSOPHY & FUN OF ALGEBRA, Chapter 16, Infinity, part 1

Chapter 16, Infinity, part 1

You remember the angel who looks like this, −1. Now I am going to introduce you to another angel. It is called “Infinity.” When you come to it, remember what I told you before—Angels are messengers from the great world of the “As-Yet-Unknown.” They never gossip about their private affairs, or those of other angels. They come to tell you either about what you are to do next, or about something you had better not do next; and if you ask them impertinent questions about things that do not concern you for the time being, they will give you headaches and make your head spin: just to teach you to mind your own business. This particular angel always comes with a message about a broken link or a loosened chain. It comes, when an hypothesis has been fully worked out, to tell you that you are now free from the bonds of that hypothesis and at liberty to start experimenting on a fresh one. But its message is never: “You have got out of that particular house of bondage and therefore you may, for all the rest of your life, run riot, and eat, and drink, and do, whatever you please.” Its message always is: “You have outgrown that master; now you may take a holiday and have a fling before you go into a higher class; but, just because you are set free, look out for danger traps; and mind your Ten Commandments.”

You will understand Infinity's messages better if you will read carefully what is written about it in Chapter XV. of “The Logic of Arithmetic.” It brought the answer to the question: “How many children could pass through a school-room without the apples all being eaten up, supposing that none of the children ate any?” Let us go over that ground again. Suppose there is a cake on the table. How many children can go through the room without the cake being all eaten up?


Chapter 16, Infinity, part 1 Kapitel 16, Innigkeit, Teil 1 Capítulo 16, Infinidad, parte 1 Capítulo 16, Infinity, parte 1

You remember the angel who looks like this, −1. Lembras-te do anjo que se parece com este, -1. Now I am going to introduce you to another angel. Agora vou apresentar-vos outro anjo. It is called “Infinity.” When you come to it, remember what I told you before—Angels are messengers from the great world of the “As-Yet-Unknown.” They never gossip about their private affairs, or those of other angels. Chama-se "Infinity". Quando chegar a ele, lembre-se do que lhe disse antes - os Anjos são mensageiros do grande mundo do "As-Yet-Unknown". Nunca fazem mexericos sobre o seu affairs privado, ou sobre os de outros anjos. They come to tell you either about what you are to do next, or about something you had better not do next; and if you ask them impertinent questions about things that do not concern you for the time being, they will give you headaches and make your head spin: just to teach you to mind your own business. Eles vêm dizer-te ou sobre o que deves fazer a seguir, ou sobre algo que é melhor não fazer a seguir; e se lhes fizeres perguntas impertinentes sobre coisas que não te dizem respeito por enquanto, eles dar-te-ão dores de cabeça e farão a tua cabeça girar: apenas para te ensinarem a meter-te na tua própria vida. This particular angel always comes with a message about a broken link or a loosened chain. Este anjo em particular vem sempre com uma mensagem sobre um elo quebrado ou uma corrente solta. It comes, when an hypothesis has been fully worked out, to tell you that you are now free from the bonds of that hypothesis and at liberty to start experimenting on a fresh one. Vem, quando uma hipótese tiver sido completamente trabalhada, dizer-lhe que está agora livre dos laços dessa hipótese e que tem a liberdade de começar a experimentar uma nova. But its message is never: “You have got out of that particular house of bondage and therefore you may, for all the rest of your life, run riot, and eat, and drink, and do, whatever you please.” Its message always is: “You have outgrown that master; now you may take a holiday and have a fling before you go into a higher class; but, just because you are set free, look out for danger traps; and mind your Ten Commandments.” Mas a sua mensagem nunca é: "Saíste daquela casa particular de servidão e, portanto, podes, para o resto da tua vida, correr de motim, comer, beber, e fazer, o que quiseres". A sua mensagem é sempre a seguinte: "Já superaste esse mestre; agora podes tirar férias e ter um fling antes de entrares para uma classe superior; mas, só porque estás livre, procura armadilhas de perigo; e tem em conta os teus Dez Mandamentos".

You will understand Infinity's messages better if you will read carefully what  is written about it in Chapter XV. Compreenderá melhor as mensagens do Infinity se ler atentamente o que está escrito sobre o mesmo no Capítulo XV. of “The Logic of Arithmetic.” It brought the answer to the question: “How many children could pass through a school-room without the apples all being eaten up, supposing that none of the children ate any?” Let us go over that ground again. de "A Lógica da Aritmética". Trouxe a resposta à pergunta: "Quantas crianças poderiam passar por uma sala de aula sem que as maçãs fossem todas comidas, supondo que nenhuma das crianças comesse"? Vamos rever esse terreno. Suppose there is a cake on the table. Suponha que há um bolo em cima da mesa. How many children can go through the room without the cake being all eaten up? Quantas crianças podem atravessar a sala sem que o bolo seja todo comido?