I mean, a quantum computer could do it WAYYY faster (regular computers work in zeros and ones to store data, quantum computers can store in between zero and one, thus allowing more possible calculation power)
Numbers appear in DNA? You do know that stupid people will take that at face value and stunt scientific thought and curiosity, right? I mean, we still have MILLIONS of creationists and flat earthers amongst us…
So what does it mean for a number to "have no end"?
I think we are all familiar with natural numbers, zero and integrers (possitive and negative whole numbers) pretty intuitively.
Then, we made quite a big logical leap by introducing fractions.
The first fractions humanity ever mentions were reciprocal of integers. Numbers like 1/2 or 1/5, which basically mean "a number that you need this many of to get 1".
Then, humanity become more comfortable with having a bunch of those, without actually getting to one.
A number like 2/5 is therefore interpreted as "2 copies of the number you need 5 of to get 1" or "a number you need 5 copies of to get 2".
We can generalize these kinds of numbers as numbers of the form n/m , where n and m are botg integeres and mβ 0. Those are called rational numbers. In fact, the world ratio is derived from this exact term.
So, did we cover all numbers?
Apparently no.
For example, by the pythagorean theorem, thrre must be a number who’s square is the number 2, since a triangle with sidelengths 1 each must satisfy this theorem. The length of it’s hypotenuse is therefore sqrt(2), a number whose square equals to 2.
It is possible, and quite simple, to show that this number cannot be rational. Therefore, there exist a number, namely sqrt(2), which cannot be expressed as a ratio between two integers.
This is just one example of countless such numbers, and proofs showing numbers like Ο and e are not rational either.
Let’s go back to the original question, what does it mean that a number has no end?
For any two possitive numbers a,b , if a<b then aΒ²<bΒ² and vice versa.
1Β²=1 < 2 < 4=2Β²
So therefore 1 < sqrt(2) < 2 , so sqrt(2) is definitly finite. What makes it to have no end?
Well, for that we gotta understand what a decimal point means.
This number is just a sum of rational numbers. By using the lowest common denominator, we can see that we can also express it as
0.123 = 123/1000
Which is in itself a rational number. And indeed, a finite sum of rational numbers is always rational for this exact reason.
Because of that, any number expressed with a decimal point and which has a finite ammount of digits MUST be a rational number.
Not only that, it is independent on which counting system we use. We could work with binar or hexadecimal counting system, or any other, and in all of those an irrational number will have infinite amount of digits.
But what does it even mean to have infinite digits?
That’s our best attempt at representing the number, using rational numbers only. To say that 3.14 are the number with the first two digits of Ο, means that this is the biggest number with two digits after the decimal point, which is still smaller than Ο. By repeating this process over and over, adding more and more digits, we get closer and cliser to Ο from bellow.
We could do the same process for any other irrational number.
This is in fact a valid way to represent those numbers, since each irrational number has such representation, and no two distinct numbers share the same decimal representation.
Therefore, the infinity in irrational numbers comes from our attempt to represent them using something they are not – with rational numbers
The ultimate waste of time
Whoever found out about pi must be feeling aura
It isnt that important as you may think. Nasa uses only 15 DIGITS of PI.
I am so proud of myself to guess that it was pi
This is why I pay for internet
Ayy I got it right as soon as you said structure of DNA and then I saw a planet. I realize weβre talking about circumference.
I mean, a quantum computer could do it WAYYY faster (regular computers work in zeros and ones to store data, quantum computers can store in between zero and one, thus allowing more possible calculation power)
watching memes then Bam!
Numbers appear in DNA? You do know that stupid people will take that at face value and stunt scientific thought and curiosity, right? I mean, we still have MILLIONS of creationists and flat earthers amongst us…
Said the first line, knew it was Pi
Itd be funny if that one channel named pi commented on this video
Imagine if we found out that pi was actually a rational number with the new quantum computers (With trillions and trillions of digits, but still).
these numbers are called transendental number including pi and e both being the most famous
What does calculating all these pi digits even do
What was the last digit
Whatβs the point of pi?
How do we know how Pi numbers are accurate
Supercomputer: Whatever game you’re playing, you can’t defeat me π
Human: Oh I know.. but he can π
**Opens Minecraft and sets Render Distance to 1024 chunks with RTX**
Imagine how crazy everybody would go if pi suddenly just ended, like we calculated it to the end
So what does it mean for a number to "have no end"?
I think we are all familiar with natural numbers, zero and integrers (possitive and negative whole numbers) pretty intuitively.
Then, we made quite a big logical leap by introducing fractions.
The first fractions humanity ever mentions were reciprocal of integers. Numbers like 1/2 or 1/5, which basically mean "a number that you need this many of to get 1".
Then, humanity become more comfortable with having a bunch of those, without actually getting to one.
A number like 2/5 is therefore interpreted as "2 copies of the number you need 5 of to get 1" or "a number you need 5 copies of to get 2".
We can generalize these kinds of numbers as numbers of the form n/m , where n and m are botg integeres and mβ 0. Those are called rational numbers. In fact, the world ratio is derived from this exact term.
So, did we cover all numbers?
Apparently no.
For example, by the pythagorean theorem, thrre must be a number who’s square is the number 2, since a triangle with sidelengths 1 each must satisfy this theorem. The length of it’s hypotenuse is therefore sqrt(2), a number whose square equals to 2.
It is possible, and quite simple, to show that this number cannot be rational. Therefore, there exist a number, namely sqrt(2), which cannot be expressed as a ratio between two integers.
This is just one example of countless such numbers, and proofs showing numbers like Ο and e are not rational either.
Let’s go back to the original question, what does it mean that a number has no end?
For any two possitive numbers a,b , if a<b then aΒ²<bΒ² and vice versa.
1Β²=1 < 2 < 4=2Β²
So therefore 1 < sqrt(2) < 2 , so sqrt(2) is definitly finite. What makes it to have no end?
Well, for that we gotta understand what a decimal point means.
For example, the number 0.123
0.123 = (0 * 1) + (1 * 1/10) + (2 * 1/100) + (3 * 1/1000)
This number is just a sum of rational numbers. By using the lowest common denominator, we can see that we can also express it as
0.123 = 123/1000
Which is in itself a rational number. And indeed, a finite sum of rational numbers is always rational for this exact reason.
Because of that, any number expressed with a decimal point and which has a finite ammount of digits MUST be a rational number.
Not only that, it is independent on which counting system we use. We could work with binar or hexadecimal counting system, or any other, and in all of those an irrational number will have infinite amount of digits.
But what does it even mean to have infinite digits?
That’s our best attempt at representing the number, using rational numbers only. To say that 3.14 are the number with the first two digits of Ο, means that this is the biggest number with two digits after the decimal point, which is still smaller than Ο. By repeating this process over and over, adding more and more digits, we get closer and cliser to Ο from bellow.
We could do the same process for any other irrational number.
This is in fact a valid way to represent those numbers, since each irrational number has such representation, and no two distinct numbers share the same decimal representation.
Therefore, the infinity in irrational numbers comes from our attempt to represent them using something they are not – with rational numbers
I donβt get how a number could be that longβ¦ liek why doesnβt it end?
the 2009 record is 2.7 terabytes of just numbers
Sooooo⦠When is nerve gear dropping?
This means the circumference of a circle cannot be completely calculated.
create supercomputers to:
send people to other planetsβ
do analytic geometry β
simplify quantum mechanics β
find piβ
Yeah thats cool and whatever but how does this helo pay my rent and buy food?
Does any digit show up more than others do in pi?
No, its 42
Itβs 42
Chud
Using the algorithm and a program called y crunch i got a normal pc with 16gb of ram to calculate 10b digits
You suck
The kind of work trolls put in to make their 3.9 Zettabyte zipbomb:
Maybe quantum PCs could calcutale a until infinite π
How do we verify that these digits are actually correct?
if you will comsult the algorithm you will find that nothing ever happens
What if one day pie ends and we all go hungry
I think its 8
I don’t get why it’s such a big deal. I know every digit of pi.
Bro they better finish soon I need it to predict the stock market ππ»ππ»
Idk why people have such a obsession with pie. If you really need to break a infinite number down do 100/3 for eternity.
WHAT 314 COMMENTS
Imagine one guy deletes the 31 millionth number and they gotta find which one missing
Me when I tell my math teacher pi can be rounded to 3 π½
The school librarian was NOT happy when I tried to print 1,000 pages of Pi back in 2002….
Most nunbers do not have an end to them. We’re just more familiar with rationals because we use them more in every-day life.
I like your words magic man
Chud
42
How precise do we need it to be