At 4:13, I say that because √2 is irrational, then it must contain every possible string of integers such as your phone number. This was wrong. To have that property, a number must be both irrational AND normal. While it has been proven that almost all real numbers are normal, and it is widely believed that √2 is one of them, a proof still has not been discovered. It's not difficult to think of a number that is irrational, yet does NOT contain every possible string of integers. One example is 1.0101101110111101111101111110... I apologize for the mistake. Thank you all for watching and for helping me grow my channel.
I had the exact same thought as you were saying that your phone number is embedded within the never ending sequence of digits when you take the square root of two. This is not a statement that you can make without a proof, and intuitively, it is not necessarily guaranteed that a specific sequence of numbers must be there, just because the irrational number continues on forever.
It’s not necessarily true that all strings of numbers are in sqrt(2). That property is called normality and it is exceptionally difficult to prove normality. We do not know that sqrt(2) is normal
If a decimal terminates, then it can easily by written as a fraction with some power of 10 as the denominator. If it repeats, then it can also be written as a fraction, but with a denominator of one less than a power of 10.
At 4:13, I say that because √2 is irrational, then it must contain every possible string of integers such as your phone number. This was wrong. To have that property, a number must be both irrational AND normal. While it has been proven that almost all real numbers are normal, and it is widely believed that √2 is one of them, a proof still has not been discovered. It's not difficult to think of a number that is irrational, yet does NOT contain every possible string of integers. One example is 1.0101101110111101111101111110...
I apologize for the mistake. Thank you all for watching and for helping me grow my channel.
I had the exact same thought as you were saying that your phone number is embedded within the never ending sequence of digits when you take the square root of two. This is not a statement that you can make without a proof, and intuitively, it is not necessarily guaranteed that a specific sequence of numbers must be there, just because the irrational number continues on forever.
Hi, the video is awesome. Can you tell us the editors and any other softwares which you use while making them? Thanks!
I use a combination of different programs, like PowerPoint, OBS, Wondershare, etc.
This proof is so complicated man. It looks simple but the discoverer must have thought so deeply
Add to that that there was no algebra back in that day...
Made very easy to be understood.. 👍
this is the clearest explanation by far
Thank you 🙏
MY FAVE SO FAR! Now I want you to teach me History !
It’s not necessarily true that all strings of numbers are in sqrt(2). That property is called normality and it is exceptionally difficult to prove normality. We do not know that sqrt(2) is normal
You are absolutely right, and I regret that I made that mistake. I already addressed it in the comments. Thank you for your input.
@@LearnPlaySolve ah, sorry , hadn’t seen it but makes sense. Great video all the same!
extremely nice way of teaching
Thank you!
As the bissection is always possible for all line segments, 2 is always a factor.
Awesome video so creative!!!!
Now I know what a Rational Number is! And also not to proof at sea
thanks for the video
Thanks Bro😀
Great help 🙌
Whao! It was awesome
why decimal representation of irrational numbers is non terminating non reapeating 💯💯💯💯💯💯💯💯💯💯
If a decimal terminates, then it can easily by written as a fraction with some power of 10 as the denominator. If it repeats, then it can also be written as a fraction, but with a denominator of one less than a power of 10.
Ratio'd
It was a triangle.