
Infinity
Infinity is something we are introduced to in our math classes, and later on we learn that infinity can also be used in physics, philosophy, social sciences, etc. Infinity is characterized by a number of uncountable objects or concepts which have no limits or size. This concept can be used to describe something huge and boundless. It has been studied by plenty of scientists and philosophers of the world, since the early Greek and early Indian epochs. In writing, infinity can be noted by a specific mathematical sign known as the infinity symbol (∞) created by John Wallis, an English mathematician who lived and worked in the 17th century.
The infinity symbol (∞) represents a line that never ends. The common sign for infinity, ∞, was first time used by Wallis in the mid 1650s. He also introduced 1/∞ for an infinitesimal which is so small that it can’t be measured. Wallis wrote about this and numerous other issues related to infinity in his book Treatise on the Conic Sections published in 1655. The infinity symbol looks like a horizontal version of number 8 and it represents the concept of eternity, endless and unlimited. Some scientists say, however, that John Wallis could have taken the Greek letter ω as a source for creating the infinity sign.
Overall, there are three major applications of infinity symbol:
- the mathematical
- the physical
- the metaphysical
quotes about infinity
“Two things are infinite: the universe and human stupidity; and I’m not sure about the universe.”
― Albert Einstein
«Երկու բան անսահման են. Տիեզերքը և մարդու հիմարությունը. և ես վստահ չեմ տիեզերքի մասին »:
- Ալբերտ Այնշտայն
“Some infinities are bigger than other infinities.”
― John Green
«Որոշ անսահմանություններ ավելի մեծ են, քան մյուս անսահմանությունները»:
- Ջոն Գրին
“And in that moment, I swear we were infinite.”
― Stephen Chbosky
«Եվ այդ պահին ես երդվում եմ, որ մենք անսահման ենք»:
- Ստեֆան Չբոսկին
“If the doors of perception were cleansed every thing would appear to man as it is, Infinite. For man has closed himself up, till he sees all things thro’ narrow chinks of his cavern.”
― William Blake
«Եթե ընկալման դռները մաքրվեին, ամեն բան մարդուն կհայտնվեր այնպես, ինչպես կա, Անսահման: Որովհետև մարդն ինքն իրեն փակեց, մինչև չտեսնի ամեն ինչ իր պոռնիկի նեղ խորշերից »:
- Ուիլյամ Բլեյք
“It seemed like forever ago, like we’ve had this brief but still infinite forever. Some infinities are bigger than other infinities.”
― John Green
«Թվում էր, թե հավերժ առաջ է եղել, կարծես մենք ունեցել ենք այս հակիրճ, բայց դեռևս անսահման հավերժ: Որոշ անսահմանություններ ավելի մեծ են, քան մյուս անսահմանությունները »:
- Ջոն Գրին

Five incredible facts about infinity
1.Infinity plus one
magine an infinite hotel with rooms numbered 1, 2, 3, 4 and so on forever. Even if it was full you could always fit in another guest — just ask all the old guests to move up one room, leaving room 1 free for the new guest. However, this does cause an infinite hassle, as all the guests have to move rooms.
2.Bigger than infinity?
Some infinities are bigger than others. The smallest infinity is how many whole numbers there are: 1, 2, 3, 4 and so on forever. If we include fractions there are infinitely many more numbers. In fact there are infinitely many fractions in between each whole number. But overall there aren’t more numbers unless we include the irrational numbers, the “decimals that go on forever”. There are two to the power of infinity of those, that is, 2 x 2 x 2… multiplied infinitely many times. The mathematician Georg Cantor proved that this is bigger than infinity, whatever kind of infinity you start with.
3.Zeno’s paradox
A day has only a finite number of hours and a finite number of minutes, but you do infinitely many things every day. Even just to walk over to the fridge you cover an infinite number of distances: first you have to cover half the distance, then half the remaining distance, and half the remaining distance, and so on forever. Fortunately, you can cover those infinitely many distances in finite time, otherwise you’d be infinitely hungry. This is Zeno’s paradox, and wasn’t really resolved until the invention of calculus a couple of thousand years after Zeno died.
4.Another world
You might think 1/0 is infinity. But it isn’t. But also it is. How can those both be true? It depends what mathematical world you’re in. In the world of ordinary numbers, dividing by zero can’t be defined. If 1/0 had an answer, then everything would collapse to zero. But there is a mathematical world called the extended complex numbers in which we can define 1/0 to be infinity without everything collapsing. This shows us that maths isn’t all about right and wrong, but about investigating different possible worlds in which different things can be true.
5.Complex relationships
If we were immortal we could procrastinate forever. There is actually a mathematical version of this, which is a theorem I have proved. My research is in higher-dimensional category theory, which involves studying relationships between things, relationships between relationships, relationships between relationships between relationships, and so on. In finite dimensions you have to stop at some point and decide which relationships count as equivalent. Those decisions are mathematically difficult. Whereas in infinite dimensions you can put off the decision forever. This means that the infinite dimensional category is easier to work with than the finite one. It is satisfyingly weird.