Yes but it doesn’t proof that the square root of two wasn’t invented by people because he didn’t proof that this special kind of triangle can emerge naturally. But at least squares can emerge naturally and the ratio of the diagonal and the edge of a square is the square root of two. Sodium chloride has a cubic crystal system and the surface of a cube is made out of squares.
Well, ancient math was grounded on logic, which is what philosophers use, as are most sciences, going as far as using geometry as proof. And mind you, the introduction of, and hence the acceptance of negative numbers and zero were much more recent than you would think (if you would just look at the centuries, you'd see that 2000-2099 is the 21st century all because the Greeks or Romans do not have the concept of zero), and as with the spread current number system that we use today. The name imaginary numbers was a comment of disdain by famous mathematicians of the time when it was first conceptualized, but now it had apparently allowed us to build technology faster by embracing the fact that "real" numbers are insufficient to describe the universe. If I'm not mistaken, all of these concepts were well within the last 1000 years, and I believe although knowledge is spreading and advancing really fast, there is just so much we can learn or teach that we end up graduating and working all the while not seeing the relevance of the math subjects nor the beautiful history, philosophy and logic behind them.
This is... deliciously digestible. I'm sure this took a lot of work for you to distil this information down to what you presented here, I appreciate it very much.
Professor Dave, do you have any worksheets to accompany this? I wish I could print your chart out with little descriptors. In the meantime I will make this on my own, thank you so much.
First, thank you sincerely, since you put me on the track of learning mathematics, something i was trying unsuscessfuly for a long time . Second, it would be more acurate (althoug not completely) to have the philosopher on the right, whom is Aristotle, pointing out the existence of irrationality in the numbers realm and the one on the right, whom is Plato, getting nuts about it. The one who is said to be annoyed was Pythagoras but Plato belived in the ideal existence of perfect forms so it is good enough. Thank you again!!!
0.999... (infinitely recurring) is just another way to write 1. 0.999... is the same as 1, the same way 1 is the same as 2/2, because 1 - 2/2 = 0. There is no difference between the numbers. 0.999... - 1 = 0 too, because it is the same number. Intuitively you think it has to be 0.0...01, because at _some_ point _surely_ it stops. But it is infinitely recurring, so it never stops. It extends forever, but our brains can't process that concept. There is no number that exists that can come between 0.999... and 1, because there is no difference.
@@James-hs1eq I still am waiting but still can’t wait to use the information in my life, it will be so great to have this knowledge in a situation where a number is irrational or imaginary and not real but will be able to identify that because I learned about these types of numbers, it will be so worth it for moments like those yknow
@@James-hs1eq you just never know when you need to know if the number you’re looking at is real or not, and it’s really important to know if it is. Taxes? Bills? Preparation for adulthood? None of that is as important than this bro, this is like life changing information tbh
It would seem for root 2 to exist, it requires lines to be constructed with 0 thickeness or width. However such lines are difficult to see. On any physical construction of a triangle, the perimeter of the triangle will be different along the outer edge compared to the inner edge. And then which one is root 2 the outer edge or the inner edge? So it would seem to me that it’s just a mathematical concept. We can draw a very accurate approximation, but true mathematical perfection only exists on the paper.
I really would like to know how 9/9 is.9999999999999 and not 1 if 9 goes into 9 one time and if .999999999999999 equals 1? Why doesn't the computer just say 1???😊
You are saying that 9/9 = 0.999999999... which = 1, I can't understand why that? It's just obvious that giving 9 apples to 9 number of people means everyone has one. So how decimals can exist here? I'm waiting for the answer from you porfessor. However, I love this channel, it really makes things as easy as 1+1. Never knew it's so easy and never felt so interested in math like now, although i was interested in it before too!
Hey I have another explanation, if u mind checking on it Actually 1/9 = 0. 1111... and so if we multiply it by 9 on both sides of the equation, we have 9/9 = 0.9999... I hope this helps u
The definition of the square root a real number y is the *non-negative* real number x such that x^2 = y, and the relation x |-> "square root of x" is a function, so the output is unique. It does not have two outputs.
Would you say that an irrational number is really a real number? After all irrational numbers such as pi and square root of 2 are formula generated values and can not be exactly pinpointed on a number line.
Without other information, yes. Irrational numbers that lie on the real number line, are real numbers. There are imaginary and complex numbers that are irrational, so not all irrational numbers are real. But if a number's defining characteristic is that it is irrational, and no one bothered to specify if part of it is imaginary, most likely, it is a real number. The terms integer, rational, irrational, algebraic, and transcendental, all refer to how the number fits between previously understood classifications numbers on the real number line, unless otherwise specified that it is non-real. The terms real and imaginary, refer to which number line it resides upon, with complex referring to a sum of real and imaginary.
I get it now! This is precisely how irrational numbers work! No matter how much we hate and loathe irrational numbers they'll still continue to exist! -definitely not 37
![The most beautiful equation in math, explained visually [Euler’s Formula]](http://i.ytimg.com/vi/f8CXG7dS-D0/mqdefault.jpg)
I've been struggling at every single lesson in my math class, but when professor dave explains ANYTHING
its as easy as 1+1
Really 😮🥺 not for me
@@A_Good_Boy. yeah this stuff is confusing
How old are you@@RefRed_King
@@Frunktown 18 btw 22 mins ago is crazy
"This triangle exists, and therefore, root 2 exists"
You sound like an ancient philosopher
Yes but it doesn’t proof that the square root of two wasn’t invented by people because he didn’t proof that this special kind of triangle can emerge naturally.
But at least squares can emerge naturally and the ratio of the diagonal and the edge of a square is the square root of two.
Sodium chloride has a cubic crystal system and the surface of a cube is made out of squares.
@@plantae420 dude i commented this a year ago
@@lawsonrhea4834 time is imaginary so Plantae saw your past post in his present
@@solarsystem1605 more like relative. not imaginary
Well, ancient math was grounded on logic, which is what philosophers use, as are most sciences, going as far as using geometry as proof. And mind you, the introduction of, and hence the acceptance of negative numbers and zero were much more recent than you would think (if you would just look at the centuries, you'd see that 2000-2099 is the 21st century all because the Greeks or Romans do not have the concept of zero), and as with the spread current number system that we use today. The name imaginary numbers was a comment of disdain by famous mathematicians of the time when it was first conceptualized, but now it had apparently allowed us to build technology faster by embracing the fact that "real" numbers are insufficient to describe the universe. If I'm not mistaken, all of these concepts were well within the last 1000 years, and I believe although knowledge is spreading and advancing really fast, there is just so much we can learn or teach that we end up graduating and working all the while not seeing the relevance of the math subjects nor the beautiful history, philosophy and logic behind them.
"Imaginary numbers don't exist, they can't hurt you"
_i_
Quaternions
Mfs when x^2 is a negative: 😨
i = -1
-i = 1
@@Johnathan9743dumb
This is... deliciously digestible.
I'm sure this took a lot of work for you to distil this information down to what you presented here, I appreciate it very much.
This is the best explanation I’ve found thank you so much!
Good explanation....... Forgot all these in busy life
No I have no baby 🍼
Hello sir!
Sir I’m trying to improve my math and take out my math fear and i guess I’m just at the right channel. Thank you sir
One of the best channels existed yet!
The intro is 🔥🔥🔥
This is a grade-saver! Thanks!
Thank you so much i have been doing bad in math class until I started watching your channel
You are the best professor
These videos are so helpful.
Thank you for the chart. I think my students will understand this much better now. :)
I tried this one to my students. This also a good help.
th-cam.com/video/lchnm_-8WgI/w-d-xo.html
This is beautifully explained. Thanks 😊
Thanks for the update
A save once again. Thanks professor 🥹🙏🏻
Thank u for the session professor Dave!
you explained it so simply
This is perfect explanation!)
Professor Dave, do you have any worksheets to accompany this? I wish I could print your chart out with little descriptors. In the meantime I will make this on my own, thank you so much.
Thanks for sharing your knowledge of maths.
First, thank you sincerely, since you put me on the track of learning mathematics, something i was trying unsuscessfuly for a long time . Second, it would be more acurate (althoug not completely) to have the philosopher on the right, whom is Aristotle, pointing out the existence of irrationality in the numbers realm and the one on the right, whom is Plato, getting nuts about it. The one who is said to be annoyed was Pythagoras but Plato belived in the ideal existence of perfect forms so it is good enough. Thank you again!!!
Thank you!!! You summed it up perfectly and not in an annoying way like some.
6:27
Adm! The sir said that 9 ÷ 9 = 0.999.., it's wrong, all number divided by himself is exactly one.
0.999... (infinitely recurring) is just another way to write 1.
0.999... is the same as 1, the same way 1 is the same as 2/2, because 1 - 2/2 = 0. There is no difference between the numbers.
0.999... - 1 = 0 too, because it is the same number. Intuitively you think it has to be 0.0...01, because at _some_ point _surely_ it stops. But it is infinitely recurring, so it never stops. It extends forever, but our brains can't process that concept.
There is no number that exists that can come between 0.999... and 1, because there is no difference.
You are right. But actually
1/9 = 0. 1111...
and so if we multiply it by 9 on both sides of the equation, we have
9/9 = 0.9999...
I hope this helps u
do it on your calculator. Divide 1 by 9, you get 0.1111... then multiply it by 9, you will get 1 instead of 0.999... Hehe, it's not wrong :D
I wish you sir for 1 million subscribers
Sorry for bad english
Your wish came true
Thanks for the video❤
Thanks, Prof
Wow sir now I understand very quickly thanks sir 😊
Thabkyou i have a test tomorrow this helps alot 👍
Good explanation 5/5 💖
i am a student from mexico, professor Dave explain much better than my professor.
When you explain what is essentially a whole lecture at school in 9 minutes
thank u so much im late but this helps now
Your explanation is mind blowing sir
great video. I was confused weather imaginary number is irrational or not, but it was solved by you. Thank you.
Good job brother ☺️
Who is watching this because they have an exam soon
me
Yes,please how do u know it
Me
Tomorrow 😢
Me tomorrow
Educational for us👌
As a college student, this video has been helpful to me
Professor thank you for your hard work❤
I can’t wait to use this information in my life
Update?
@@James-hs1eq I still am waiting but still can’t wait to use the information in my life, it will be so great to have this knowledge in a situation where a number is irrational or imaginary and not real but will be able to identify that because I learned about these types of numbers, it will be so worth it for moments like those yknow
@@James-hs1eq you just never know when you need to know if the number you’re looking at is real or not, and it’s really important to know if it is. Taxes? Bills? Preparation for adulthood? None of that is as important than this bro, this is like life changing information tbh
@@Ilovebrushingmyhorse Sarcasm 100 lmao
can you please tell how he estimated the stated fraction of square root 2?
Thank you, it was pretty useful 👌☺
Sir please tell that what you say after ''Support me on patreon?''
support me on patreon so i can keep making content! i need a little help with the cost.
@@ProfessorDaveExplains Sir we need more professors like you. I can give my support by watching your videos.
finalllyyy. I finish algebra 1😊
This video really helped me thank you so much
Best explanation indeed!
The song was amazing and explaination is more awesome.Thanks Professor
thanks prof .
Thanks a lot, Sir
Ooh so that’s how gojo’s power works.
Nice explanation. Tnk u sir..
Thanks Dave..... This would help my child a lot...... Love from India
Hello profesor dave, I didn’t know you make Math classes too. Thank you, i learned a lot from your videos
Excellent!
Thanks sir this help me too much
Explaination was very clear
Great!!!!!!!!!! 👍👍👍
1- rational numbers
2- irrational numbers
3- it's undefined or imaginary numbers
4- natural numbers (1,2,3,..
5- all irrational numbers are real numbers
❤👌Professor.
Love from India!
Hats off to yout teaching style 🙇
It would seem for root 2 to exist, it requires lines to be constructed with 0 thickeness or width. However such lines are difficult to see.
On any physical construction of a triangle, the perimeter of the triangle will be different along the outer edge compared to the inner edge. And then which one is root 2 the outer edge or the inner edge?
So it would seem to me that it’s just a mathematical concept. We can draw a very accurate approximation, but true mathematical perfection only exists on the paper.
I will never forget this 😉
Professor Dave explains very well 🤗
Great video! Thanks Professor.
Sent here by my math teacher
Nice explanation
Thank you professor : )
Precise and well explained!! Thanks a ton!!
What is decimal piont 🤔
I really would like to know how 9/9 is.9999999999999 and not 1 if 9 goes into 9 one time and if .999999999999999 equals 1? Why doesn't the computer just say 1???😊
Thank Professor
yo my teacher is making me watch this and this is the first video that i actually understood what they were talking about so thanks
What about Transcendental numbers?
Your voice is just awesome
I HAVE NOW CONQUERED ALGEBRA...1. I've conquered Algebra 1. ONTO THE NEXT ADVERSARY!
Thank you this is very helpful.
This is also helpful.
th-cam.com/video/lchnm_-8WgI/w-d-xo.html
You finna hit a milli congratulations
You are saying that 9/9 = 0.999999999... which = 1, I can't understand why that? It's just obvious that giving 9 apples to 9 number of people means everyone has one. So how decimals can exist here?
I'm waiting for the answer from you porfessor.
However, I love this channel, it really makes things as easy as 1+1. Never knew it's so easy and never felt so interested in math like now, although i was interested in it before too!
There is no number that could ever exist between 0.9 repeating and 1, therefore they are the same number.
Hey I have another explanation, if u mind checking on it
Actually
1/9 = 0. 1111...
and so if we multiply it by 9 on both sides of the equation, we have
9/9 = 0.9999...
I hope this helps u
@@ProfessorDaveExplains please use a calculator and check if 9/9 equals 1 or not(0.9999999)
@@mathmistico - Come on you know 9/9 is 1 . If you multiply incorrect\incomplete answers the issue will just magnify
A very good clear explanation of this confusing topic!
Isn't the square of any positive number both negative and positive ?
Nope
Minus multiplied with minus gives plus
Actually it square root of positive numbers is both positive and negative
@@abstractguy9 No, it is not. While the equation x^2 = y has two solutions, only one of those two solutions is actually called the square root.
The definition of the square root a real number y is the *non-negative* real number x such that x^2 = y, and the relation x |-> "square root of x" is a function, so the output is unique. It does not have two outputs.
Would you say that an irrational number is really a real number? After all irrational numbers such as pi and square root of 2 are formula generated values and can not be exactly pinpointed on a number line.
Without other information, yes. Irrational numbers that lie on the real number line, are real numbers.
There are imaginary and complex numbers that are irrational, so not all irrational numbers are real. But if a number's defining characteristic is that it is irrational, and no one bothered to specify if part of it is imaginary, most likely, it is a real number.
The terms integer, rational, irrational, algebraic, and transcendental, all refer to how the number fits between previously understood classifications numbers on the real number line, unless otherwise specified that it is non-real. The terms real and imaginary, refer to which number line it resides upon, with complex referring to a sum of real and imaginary.
I get it now! This is precisely how irrational numbers work! No matter how much we hate and loathe irrational numbers they'll still continue to exist!
-definitely not 37
Good work. But 9 over 9 (9/9) equals 1 not 0.9999... , right?
Those are the same thing.
@@ProfessorDaveExplains How? They are almost equal but not equal.
thank you! very good explanation i’ll be subscribing
Tis video wasnt in "maths all of it" playlist in starting stages... why prof. Dave why... 🥺
Its a really great help thank you so much sir you helped me finished my module
I understand easily.... Thanks, professor!
In math ➗ can I say that fractions are ratios??
nice one
Best explanation I found thank u
Thank you so much♥❤😍
any numbers that can fit on number line
Nice 🎉
my brain cant comprehend this. idk what hes saying anymore.........good luck on my test
Thank u
Love you Sir,U r the Great
Is i ^ i rational or irrational?
Thank you so much you were really helpful 😊
Professor pardon my ignorance, but kindly explain again how can .99999........(infinity) be equal to 1 ?
there is no number between them, so they are the same number
It's a limit. The limit as sum of 9/10^k from k=1 to infinity will equal 1
Thank you :))