We have taken a big step forward. Now we use calculators and computers to calculate large numbers. We even gave this number a special name, and there is no limit. What is the largest number in mathematics?
Not very obvious
So, what's the maximum quantity? The answer should be obvious: infinity, right? But this is not entirely correct.
In the strictest sense, infinity is not a number. Infinity is just a concept, which means "a quantity with no constraint and no end point".
The definition of infinity in mathematics shows that no matter how big a number is, adding 1 can make it bigger. By doing this constantly, a number can always grow forever or "infinitely".
What is the maximum number used in mathematics?
The largest number used in formal mathematical proof is Graham number. It was previously listed in the Guinness Book of World Records and is the largest number in the world.
Green's constant is the upper bound solution of an extremely unusual problem in Ramsey's theory, and it is an unimaginable giant. This problem is expressed as: connecting each pair of geometric vertices of an n-dimensional hypercube to get a complete graph with 2 n vertices (a simple graph with only one edge between each pair of vertices). Fill each side of the picture with red or blue. Then, what is the minimum n value that makes all filling methods contain at least one monochromatic complete subgraph on the vertices of four * * * faces?
Ge Henry's number is so huge that it cannot be expressed by scientific notation. Even the exponential tower form like A (B (C (…)) is useless and even mathematicians can't understand it. For example, if all known substances in the universe are converted into ink and put into a pen, there is not enough ink to write all these numbers on paper. But it can be described by Gartner's recursive formula of arrow symbol.
Graham's number
Although this number is too large to be calculated completely, the last few digits of Greyhound number can be deduced by a simple algorithm. Its last 12 bit is 262464 195387.
So, what is the answer to Ronald Graham's question? According to some mathematicians, they doubt that the answer is "6"
The so-called "maximum number" is essentially the concept of "infinity". In the history of human mathematics, the concept of "infinity" has really puzzled mathematicians for a long time, and even a "mathematical crisis" has appeared, and there have been many noteworthy paradoxes, such as "Achilles paradox", which everyone should understand.
If you ask a pupil such a question, the answer is simple: there is no maximum number, which can be proved by reduction to absurdity. If there is a maximum number a, isn't A+ 1 greater than a?
Although the pupils' understanding is correct, the study and understanding of infinity in the history of human mathematics is by no means the level of "pupils' understanding". If we only stay at this level, it is difficult for human mathematics to develop today.
Simply put, infinity is just a concept, and the "maximum number" is of course a concept. There is no such number. I remember some scientists even gave this understanding: the maximum number is zero! If you refute: how can the maximum number be zero? Scientists will say: You haven't given the maximum number, how do you know that the maximum number can't be zero?
At the same time, the same infinity has its own size, and some infinity is bigger than others. This size can't be understood in our conventional way. For example, there are infinite rational numbers and infinite irrational numbers, so which is more rational and which is more irrational? The conclusion is that there are many irrational numbers (the proof method is not difficult and will not be shown here).
Also, which is more, natural number or even number? Intuitively, you might say that there are many natural numbers, because natural numbers include even numbers and odd numbers, but they are actually the same, because if you multiply all natural numbers by 2, won't the results be even numbers? This shows that every natural number has an even number corresponding to it, and of course there are so many!
Therefore, don't think about the question of "is there a maximum number", but study the concept of "infinity". This is a deep-seated problem. Designing calculus can greatly improve your thinking ability!
These so-called large numbers are a piece of cake. The biggest number belongs to him.
Can some so-called large numbers be arrogant?
mersenne prime
As we know, a prime number is an integer greater than 1 that can only be divisible by 1 and itself. There are infinitely many prime numbers, among which the number that can be called a large number is mersenne prime, and if the Mason number is a prime number, it is called mersenne prime. Mersenne prime is a big one in a short time. As the prime number gets bigger and bigger, its growth will be unimaginable. Until 195 1 year, only 12 of these prime numbers was known, but this year, there are 48 known prime numbers.
The largest known prime number before 20 13 was 257885 1 61-kloc-0/,with more than 7 million digits. But now the record has been refreshed, and only 51mersenne prime was found, the largest being M8. The book printed with this prime number reaches more than 700 pages.
General Electric Henry. In 1970s, a work done by American mathematician Ronald Ronald Graham proved to be very huge. He tried to solve a problem related to a higher dimensional cube. When he finally got the answer, he found that the numbers involved in the answer were too big for us to write down at all-if 2000 numbers were written on a page according to the thickness of A4 paper, the whole space would not be enough! It is a Gregorian constant, which is too huge to be expressed by scientific notation. Even the exponential tower form like A (B (C (…)) is useless and even mathematicians can't understand it.
Tree (3)
Although the Gregorian calendar has a large number, there is something bigger than it. Yes, the tree (3) is such a horrible existence! The tree (3) is much bigger than the Greyhound. The ratio of Green's constant to tree (3) can be ignored. Even if Ronald Graham is iterated several times, the Greer constant is infinitely small compared with the tree (3). So what is the third tree? Smart netizens should literally be related to trees.
The simple point is that you draw such a tree, first draw the first node from the root, and then add a node to each branch, requiring that the number of new nodes should not be greater than the total number of its nodes, and the color of the nodes should not be the same as the color of the first tree from the second stroke, so draw. Ok, start drawing the tree (1) first, and you will find that you have just started drawing the first node, so you can't draw it any more, because only one color is allowed, and no matter how you draw the node, it must be the same as the first tree node. Then start tree(2), and you will find that if the first tree you draw is a red node, you can only draw green branches, but if you go up to the third floor, you will repeat it in green, and you can't change it to red, because it is also repeated with the second floor, so you can only draw three strokes, namely the red node and two green nodes.
Greer's constant was once considered as the largest number in formal mathematical proof. Although it also won the Guinness Book of World Records, it was later replaced by Tree (3). However, people who think that these so-called large numbers can be called the majority completely ignore the existence of the earliest, largest and fastest large number discovered by human beings. This is the world-famous great mathematician Euclid. . . Around 300 BC, Euclid proved the infinity of prime numbers by geometric methods in his Elements of Geometry. Its main idea is to have a line segment AB, let line segment C be equal to AB, and add a little G outside line segment C. We say that G is different from A, B and C. If it is the same, it is impossible. If G is divisible by AB, then G will be divisible by C. It is expressed by the formula, namely 1X2X3X4X5X6X7. . . . . . XP x 1, expressed by formula, G=PXP 1XP2xP3. . . . . . XP X 1。 With this formula, we can find that1x2x3x5 = 3ox1= 211,1x2x3x5 ... x37 = 7.420738e12x1. 1 x2x5x5 ... x97 = 2.305568.e36 ten1. It will be ready in a few hundred minutes. If you are willing to pick up your mobile phone and use this method to calculate, it can be 1 x2x5x5 ... x127 = 4.014476E48X1. 1x2x5x5...x229 = 1.907825 e 9 1 x 1。 Some people say that the interval of prime numbers contained in positive integers of natural numbers is mysterious, and sometimes he is far away, which is unimaginable. This obscure great number theory gentleman described the interval sequence of prime numbers like this. The interval between two prime numbers contained in a positive integer of a natural number is as long as it is, which makes the interval between two prime numbers more mysterious. For example, if we want to insert a thousand complex numbers between two prime numbers, we only need 1 x2x4x5 ... x10001101. . . . . . 1x2x3x4x5...X 100 1x 100 1。