Children often ask the question: "What is the largest number?" This question is an important step in the transition to the world of abstract concepts. The answer, of course, is simple: numbers are most likely infinite, but there is a certain threshold beyond which numbers become so large that there is no point in them, except that they can technically exist. Let's take the top ten giant numbers we know, but restrict ourselves to extremely important concepts in the world of numbers.
10 ^ 80
Ten to the eightieth power - 1 followed by 80 zeros - is a pretty massive number representing the approximate number of elementary particles in the known universe, and when we say elementary particles, we don't mean microscopic particles - we are talking about much smaller things like quarks and leptons - about subatomic particles. This number in the United States and modern Britain is called "one hundred quinquavigintillion". It seems to be easy to understand that this number denotes the number of smallest particles in our universe, but this is the smallest and simplest number on our list.
One googol
The word googol, slightly modified, has become frequently used in modern times, thanks to the popular search engine. This number has an interesting history - just google it. The term was coined by Milton Sirotta in 1938 when he was 9 years old. And although this is a relatively abstract number, and its existence is explained by the need for technical existence, they still found application.
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Alexis Lemaire set a world record by calculating the root of thirteen from a hundred-digit number. Googol is a hundred-digit number, a number with a hundred zeros. It is also assumed that from one to one and a half googol years have passed since the Big Bang.
8.5 x 10 ^ 185
The Plank length is a very small length, approximately 1.616199 x 10-35, or 0.00000000000000000000000000000616199 meters. In an inch cube, these lengths are about the size of a googol. Planck length and volume play an important role in the branches of quantum physics - for example, string theory - because they allow calculations on the smallest scales. There are approximately 8.5 x 10 ^ 185 Planck volumes in the universe. This is a fairly large number, and yet it has no practical application, but it remains simple enough on our list.
2 ^ 43,112,609 - 1
The third largest number on this list is the number of all planck volumes in the universe, with 185 digits. And this number includes almost 13 million digits. Why is this number important? This is the largest prime number known today. It was discovered in August 2008 during the Great Internet Messene Prime Search (GIMPS).
Googolplex
You've probably heard that word, at least in Back to the Future, when Dr. Emmett Brown muttered, "She's one in a million, one in a billion, one in a googolplex." What is a googolplex? Remember the length of the googol? One and one hundred zeros. A googolplex is ten to the power of googol. This is more than the number of all particles in the known part of the universe.
You might notice that you can raise ten to the power of a googolplex and there will be even more, and so on, and you will be completely right.
Skewes numbers
The Skuse number is the upper limit for the mathematical problem π (x)> Li (x), although it looks simple, but it is extremely difficult in reality. Essentially, the Skuse number proves that the number x exists and breaks this rule if we assume that the Riemann hypothesis is true and the number x is less than 10 ^ 10 ^ 10 ^ 36, the first Skuse number. Even Skuse's first number is larger than a googolplex. There is also the largest Skuse number: x is less than 10 ^ 10 ^ 10 ^ 963.
Poincaré's return time
This is a very complex thing, but the basic concept is relatively simple: With enough time, anything is possible. Poincaré's return theorem assumes the amount of time that would be enough for the entire universe to return to its current state one day, caused by random quantum fluctuations. In short, "history will repeat itself." It is supposed to take 10 ^ 10 ^ 10 ^ 10 ^ 10 ^ 1.1 years.
Graham's number
In the 1980s, this number entered the Guinness Book of Records as the most massive finite number ever used in mathematical proof. It was derived by Ron Graham as an upper limit for problems in Ramsey's theory of multicolored hypercubes. The number is so large that Knuth's arrow notation (a method of writing large numbers) and Graham's own equation are used to write it. Knuth's method and how the arrows work are hard to explain, but you can imagine it like this. 3 ↑ 3 becomes 33 or 27, 3 ↑↑ 3 becomes 3 ^ 3 ^ 3 or 7,625,597,484,987. You can add another arrow to 3 ↑↑↑ 3 and go up 7.5 trillion levels. By itself, this number is significantly longer than the Poincaré return time, since you can add an infinite number of arrows and each arrow will increase the number incredibly.
Graham's number looks like this: G = f64 (4), where f (n) = 3 ↑ ^ n3. The best way to present it is to sort it out. The first layer is 3 ↑↑↑↑ 3, which is already incredibly large. The next layer is a set of arrows between the triplets. Take these arrows and place between the following triplets. This is multiplied 64 times. Even Graham himself does not know the first number, but the last ten are: 2464195387. The entire observable universe is too small to contain the usual decimal notation for Graham's number.
∞. Infinity
This number is known to everyone and everyone, it is often used for exaggeration - like some kind of "multi-million". However, this number is much more complex than most might imagine, and if you could imagine the numbers going up to this point, this number is very strange and contradictory. According to the rules of infinity, there are an infinite number of odd and even numbers at infinity, however, only half of all numbers can be even. Infinity plus one equals infinity, infinity minus one equals infinity, infinity plus infinity equals infinity, divided in half - also infinity, infinity minus infinity - no one knows, infinity divided by infinity will most likely be 1.
Scientists believe there are about 10 ^ 80 subatomic particles in the known universe, but this is only the known universe. Some have suggested that the universe is infinite. If this is so, then it is mathematically certain that there is another Earth somewhere, where each atom is folded in the same way as we and our Earth. The chance that a copy of Earth exists is incredibly small, but in an infinite universe this can not only happen, but infinitely many times.
Not everyone believes in infinity. Israeli mathematics professor Doron Zilberger argues that in his opinion, numbers will not last forever, and there will be a number so large that when you add one to it, you will come to zero. And although this number will hardly ever be discovered and hardly anyone will be able to imagine it, infinity is an important part of mathematical philosophy.
