For a specified billion bits, the probability that a billion bits starting from any bit after π decimal point are exactly the same as the specified bit is one third of 10 to the power of 10, which is a small enough but limited decimal. Because π decimal point has infinite digits, it is bound to find a billion digits exactly the same as the specified digits after a certain digit. Then, after finding this group of numbers, because π is an infinite acyclic decimal, a second group of numbers with the same billion bits will be found, thus satisfying the problem of topic setting, two repeated numbers with a length of one billion bits.
Don't worry, it's not over yet. After the second group of numbers, there are infinite acyclic numbers, and so on, the third group, the fourth group, the fifth group and so on.
If you understood the concept of infinity, you wouldn't ask such a question. No matter how large the number is, it is insignificant in the face of infinity. Let's just say that if the universe is finite, then all the basic particles of the universe-quarks-are coded by numbers one by one, and then all quarks are randomly arranged and combined, then the numbers formed by any arrangement and combination will appear as π and appear infinitely many times.
Give another infinite example. If the precision of accurate measurement can reach infinite precision, then all the knowledge in human history can be expressed by a scale on a stick with infinite precision, including all audio, video, images, words, documents, buildings, cultural relics, history, all the memories and experiences of everyone's life, and all the living things including the genetic code of each virus, and everything can be fully expressed by only one scale, which is more than enough.
Isn't it amazing?
Not necessarily!
Because I can't falsify, I say "not necessarily" instead of "definitely not". Similarly, people who can't prove it can only say "there may be" and can't say "there must be".
For example, 0.101001... is infinitely acyclic, but 1 1 can never be found, so it is wrong for some people to insist that "infinitely acyclic is everything possible".
Let me give another example, and construct an infinite acyclic decimal, which can never contain 100 million consecutive identical numbers. For example:
1. Assuming that π does not contain 100 million consecutive identical numbers, π itself conforms to the topic.
2. Assuming that π contains 1 100 million consecutive identical numbers, it is stipulated as follows: As long as 1 100 million consecutive identical numbers are encountered, they will be replaced by 50 million groups of 0 1, then the constructed new number must be infinitely acyclic and can never be found again.
At least one of 1 and 2 meets the topic, that is, an infinite acyclic decimal does not necessarily contain 100 million consecutive identical numbers.
Supplement: Someone told me the theory of infinite monkey, which is completely different from π. Infinite monkey is an infinite random number, and every bit of π is certain. Let the monkey random number 10, there are 10 possibilities, but the first ten digits of π must be 14 15926535 no matter how many times it is counted, and there is only one possibility. The conditions that infinite random numbers can meet, and infinite fixed numbers may not meet!
Figure 1 is taken from Baidu Encyclopedia, and Figure 2 is taken from the shell network.
Binary pi proved to be a normal number. Decimal numbers have not been proved to be normal numbers or composite numbers at present.
It is possible in probability, but it cannot be proved in practice.
I downloaded 1 100 million bits of pi from the Internet.
Found 7 duplicate numbers, from 0000000 to 9999999. If the probability of each number is 1/9999999, it is one in ten million. In this way, if you need 70 million digits in theory, you can find several repeated 7 digits from 0000000 to 9999999.
Then I did an experiment and copied the 100 million bits into TXT. We did find them. But when looking for 8 digits from 00000000 to 99999999, several of them were not found. Eight digits need a pi of 1 billion digits, and the computer configuration is not stuck. Conditional friends can try.
Even so, there is no proof that the number you are looking for must exist.
"Wu" faction. China ancient Zu Chongzhi, the calculation is between 3. 14 15926 and 3. 14 15927. Everyday, accurate to two is enough for us.
Then, scientists counted it to billions, and some people were still looking for it to be round. In my opinion, if two consecutive 65438+ billion bits are the same, it is definitely not a cycle. Because it has been proved that pi is a super number of infinite cyclic decimals. It can be said that 1 100 million bits is possible to cycle. Just like the sequence: 1, 1, 1. ...
May be: 1, 1, 1, 1, 1, 1. ...
It may be: 1, 1, 1, 2,3,4,6,9. ...
Therefore, the proof is the most correct.
Just like the proof of geometry, there is no doubt.
Mathematics exists in theory, not in practice. Take any number, for example, 4 needs 10 number. To repeat 4, you must have 10 numbers. In this way, 1 number can be repeated every 20 numbers. It is not difficult to work out a double-digit repetition. Want a number of 200, which is 2× 10.
This is actually a relative digital circulation problem related to pi, and it should not be, because it is generally believed that pi is infinitely acyclic, which is a fact, but it is difficult to prove it with today's scientific means.
It's a bit like throwing a pile of 10 thousand copper coins on the ground and throwing them indefinitely. Will all the same faces appear at the same time? This should be impossible, but no one can prove it theoretically.
Pi is a complicated subject. At present, human beings can't explain the principle that every decimal place of pi appears. If it can be solved, it is estimated that it is not far from uncovering the mystery of the universe, that is, human science has developed to a very high stage.
Pi is an infinite acyclic irrational number. At present, the law of its number has not been found. Don't believe some online rumors easily.