Normal Numbers Are So Weird
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- Опубликовано: 27 мар 2024
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One thing that's always bothered me, and this is such a weird math teacher thing to be bothered by, is the idea that you can find any string of digits you want somewhere in pi. Not only that, but you can find that string of digits infinitely many times. And that could be true, but we actually don't know that it's true.
If we could prove that pi were a normal number, meaning a number that, in its decimal representation, can be expected to have every digit or grouping of digits occur with equal frequency, then we could definitely say this. But no one has yet been able to prove that pi is a normal number.
#pi #normalnumbers #absolutelynormal
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Well, somebody just got doxxed
Lol
900s are reserved by the SSA. At least they were 15-20 years ago.
Some random dude in Long Island looking at their phone number in a video:
The thing is that in a truly irrational number, even if it's not normal, with infinite itterations, the probability of any set of numbers occuring however unlikely has to become a certainty.
Edit: I appreciate the education from folks, and would like to state that my comment is incorrect for anyone reading it in the future. I had a fundamental misunderstanding of the nature of irrational numbers.
Not necessarily. It is possible that, after a certain point, the number "4" just stops existing in pi. Its not likely, but we can't prove it doesnt. And if that were true, there would be some sequence requiring a 4 that didnt exist in pi.
its like how the number of squared numbers and non squared numbers are both infinite even if 1 is more rare than the other
Nope. It's all 8's after the 107 trillionth place. 🎱
Yeah no you're wrong
its not about probability, its about proofing that the set of fragments of the digits of pi contains the set of natural numbers
Why would that matter? even if there's a billion 1's for every 9, that 9 will show up eventually
If it’s not normal, we don’t know that 9 will ever show up. The equivalent for pi is that if it’s not normal, we don’t know that any particular string of digits will ever appear.
Yes but maybe never next to that 1
@@polymathematic If pi was ever proven to not be normal, would it still be possible that every string of digits appear in it at some point? Or does proving that it's not normal also prove that can't happen?
@@ethohalfslabIf Pi was ever proven to not be normal, then there would be strings of a certain length that would never appear in pi. For example all strings of length 10,000 or more with only 8's and 9's.
@@ethohalfslab i don't know! i don't know what it would look like for a number to have every digit (or string of digits) at least once, but not infinitely many times.
Thank you so much sir foe your efforts.
My phone number isn't in the first 2 million digits
maybe there is a point , googol digits out, where the 1st million digits of pi reapeat again but only by coincidence and it just continues to be random
I could watch this all day
This is how infinity works
Yeah but like… cmon.
yeah one of the best teachers on internet
You’re too kind!
You can prove that it is in pi but you can not prove that it is not in pi.
If you could prove that it is not in pi, then you couldn’t prove that it is?
@@imagod4796 for any given number you can prove it is in pi by finding it in pi. But if you don't find it, you can't prove that it is not in pi because you can't search every digit of pi
Is pi in pi? No. There- I disproved it.
Well, it is, the first digit is the first digit, the second tge second and so on
Since pi is a nonrepeating, infinite number, logically speaking you should be able to find any sequence somewhere within it. It may take several thousand years, but it logically will happen.
This feels true, but isn’t. Consider the irrational number 0.10110111011110…. It is a “non-repeating, infinite number”, and yet you’ll never find the sequence “12” in it.
@@polymathematic Yeah, but I was specifically talking about pi, which has all 10 digits in it.
Ok, imagine that same decimal, but in base 2 instead. It would use “all” the digits of base 2 (0 and 1), and it would go on forever without ever repeating, and yet it would never contain the sequence 00. The same *could* be true for pi in base 10. It certainly uses all 10 digits, but we don’t know that it uses them all with the same frequency, and we don’t know that any arbitrary sequence *must* occur. If pi is absolutely normal, that would be true, but the mere fact that pi goes on forever without repeating isn’t enough to guarantee that pi is normal.
@@polymathematic In an infinite sequence that doesn't repeat, any random string of numbers not only can exist, it must exist.
Personally, I do not have enough knowledge or care to either agree or disagree with your base 2 example. Again, my comment was about PI.
@@polymathematic Also, your example is inaccurate, if I am reading the primer on base 2 correctly. Isn't 4 denoted as 100 in base 2, which means that a sequence 00 would occur. Either that, or you are being intentionally intellectually dishonest as no number in base 2 is 00 and thus you are trying to make a statement supporting your point with an example that doesn't exist.
Personally, I don't think the second is accurate. I do not believe you are being intentionally dishonest. But, then, I tend to always look at the better side of humanity.