Infinity is an abstract concept used to describe or designate something infinite or limitless. This concept is important for mathematics, astrophysics, physics, philosophy, logic and art.
Here are some surprising facts about this complex concept that can blow the mind of anyone not very familiar with mathematics.
Infinity symbol
Infinity has its own special symbol: ∞. The symbol, or lemniscate, was introduced by the clergyman and mathematician John Wallis in 1655. The word "lemniscata" comes from the Latin word lemniscus, which means "tape".
Wallis may have based the symbol for infinity on the Roman numeral 1000, next to which the Romans used to indicate "uncountable," in addition to the number. It is also possible that the symbol is based on omega (Ω or ω), the last letter of the Greek alphabet.
An interesting fact is that the concept of infinity appeared and was used long before Wallis awarded it with the symbol that we use to this day.
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In the fourth century BC, a Jain mathematical text called the Surya Prajnapti Sutra divided all numbers into three categories, each of which in turn fell into three subcategories. In these categories, enumerable, non-enumerable, and infinite numbers were specified.
Aporia Zeno
Zeno of Elea, born around the fifth century BC e., was known for paradoxes, or aporias, including the concept of infinity.
Of all Zeno's paradoxes, Achilles and the Turtle is the most famous. In Aporia, the turtle challenges the Greek hero Achilles, inviting him to a race. The turtle claims to win the race if Achilles gives her a thousand paces advantage. According to the paradox, during the time that Achilles will run the entire distance, the turtle will take another hundred steps in the same direction. While Achilles has run another hundred steps, the turtle will have time to make another ten, and so on in descending order.
In a simpler way, the paradox is considered as follows: try to cross the room if each next step is half the size of the previous one. While each step brings you closer to the edge of the room, you will never actually get to it, or you will, but it takes an infinite number of steps.
According to one of the modern interpretations, this paradox is based on a false idea of the infinite divisibility of time and space.
Pi is an example of infinity
Pi is a great example of infinity. Mathematicians use the symbol pi for the number pi because it is impossible to write the whole number down. Pi consists of an infinite number of numbers. It is often rounded to 3.14 or even 3.14159, but no matter how many digits are written after the decimal point, it is impossible to get to the end of the number.
The Infinite Monkey Theorem
Another way to think about infinity is to consider the Infinite Monkey Theorem. According to the theorem, if you give a monkey a typewriter and an infinite amount of time, the monkey will eventually be able to print Hamlet or any other work.
While many people perceive the theorem as a demonstration of the belief that nothing is impossible, mathematicians see it as proof of the impossibility of a certain event.
Fractals and infinity
A fractal is an abstract mathematical object used in mathematics and art, most often it simulates natural phenomena. A fractal is written as a mathematical equation. Looking at a fractal, you can see its complex structure at any scale. In other words, the fractal is infinitely increasing.
The Koch Snowflake is an interesting example of a fractal. The snowflake looks like an equilateral triangle that forms a closed curve of infinite length. By increasing the curve, you can see more and more details on it. The process of increasing the curve can continue an infinite number of times. Although the Koch snowflake has a limited area, it is limited by an infinitely long line.
Infinity of different sizes
Infinity is limitless, yet it lends itself to measurement, albeit comparative. Positive numbers (greater than 0) and negative numbers (less than 0) boast infinite sets of equal-sized numbers. What happens when you combine both sets? The set will be twice as large. Or another example - all even numbers (there are infinite numbers). It is still only half the infinite number of all integers. Another example, just add one to infinity. Learn the number 1 more than infinity.
Cosmology and infinity
Cosmologists study the Universe, it is not surprising that the concept of infinity plays an important role for them. Does the universe have boundaries or is it infinite?
This question still remains unanswered. Our Universe is expanding, but where? And where is the limit of this expansion? Even if the physical universe does have boundaries, we still have a theory of the multiverse, which considers the existence of an infinite number of universes, in which there may be laws of physics different from ours.
Division by zero
There is no division by zero. It is impossible, at least in ordinary mathematics. In our usual mathematics, one divided by zero is impossible to define. This is mistake. However, this is not always the case. In the extended theory of complex numbers, dividing one by zero does not cause inevitable collapse and is determined by some form of infinity. In other words, mathematics is different, and not all of it is limited by rules from textbooks.
Hope Chikanchi