my mathematics professor would argue that sqrt(2) not in Q is not the same as sqrt(2) is irrational. we are told that the irrationals are exactly R\Q, so all real numbers which are not rational, so for example the complex number i would not be irrational, but not rational either.
Would you call √(-1) irrational? I guess I always thought of irrational numbers as being the real numbers minus the rational numbers, not just anything outside the set of rational numbers. I wonder if that's standard or just my own particularity (or even mistake!). This occurred to me in the first list of pairs of statements being evaluated as true or false. Sure, √2 is irrational and √2 is not in the set of rational numbers are both true. But it occurred to me that these might not strictly be the same claim. Thoughts?
I remember in school we learned that anything that can’t be written in the form Q/P where Q and P are integers and P doesn’t equal 0 is an irrational number. I don’t think complex numbers can be written like that. Bug then again that might just be a definition given to kids who couldn’t understand anything more complex.
I usually like to attempt these problems, often by only looking at the thumbnail and without starting the video. When I saw this thumbnail my only reaction was good grief and only in seven minutes.
"all real numbers are not rational"... it's interesting how you phrase that. it's like... (all real numbers) } rational, but the sentence most commonly reads as "all x in real numbers are not rational", which is most definitely false. strange
I think in other bases it works too. 100 in base two is equal to 8 in base ten. 10 in base two is equal to 2 in base ten. 8 is divisible by 2. in base 3: 100 = 9 in base ten 10 = 3 in base ten in base 16: 100 = 256 in base ten 10 = 16 in base ten I think no matter what number bases you're on, 100 is divisible by 10. cmiiw.
@@cepatwaras Supous you are on base k (k€N) then 10 in base k is 1*k+0=k, in the other hand if a number which ends in 0, lets call it abc...yz0 (the letters are the digits) and lets supuose it has n digits, in base ten that number is a*k^(n-1)+b*k(n-2)+...+z*k so you can factor a k subtracting one from each of the exponents. Finally cause you prove that, with the two numbers in base 10, one is a multiple of the other. Then it has to be multiple in base k aswell because the base of a number does not matter with their multiples.
@@ibrahimmassy2753 But when you write the value 256 as "100" in base sixteen, then wouldn't it mean the divisor written as "10" should also in the same base sixteen (to which the value is 16)? Therefore, 100 divided by 10 in base ten is equivalent to "100" divided by "10" in base sixteen, not "100" (base sixteen) divided by 10 (base ten). I think it's confusing when you write a mathematical sentence where a number is written on some base and another number on some other base and then you do mathematical operation on those numbers. 🙏🏼
Wish I had this baseline understanding when I started writing proofs. Great video!
Studying mathematics to optimize skywars player's suffering
I’ve seen a lot of youtubers in weird places. This is a new one for me.
Nice video, I hope to see more on formal proof writing!
4:07 I think you meant to say "Mersenne Primes". Fermat primes are of the form 2^(2^n)+1.
thought he was about to prove fermat's last theorem in under 10 minutes.
You're right!
I know... the thumbnail is for sure clickbait!! P(1) and P(2) are true, but P(n) is false for n>=3.
@@carlosgaspar8447 He was going to present a truly elegant and beautiful proof, but there wasn’t enough space on the blackboard to contain it.
Nice catch. Michael carefully places a mistake or two in every video for us to find. Kind of like easter eggs.
What you're doing is so important Mr. Penn, keep it up!
Just watch this impressive Math channel czcams.com/channels/ZDkxpcvd-T1uR65Feuj5Yg.html
the best bit was dropping the chalk in the last second
7:50
That drop of a chalk though, truly magnificent
Since "0 ∈ ℕ" is a matter of convention and can be either true or false, does that mean it isn't a mathematical statement?
Amazing video! You explained this so clearly! :)
my mathematics professor would argue that sqrt(2) not in Q is not the same as sqrt(2) is irrational. we are told that the irrationals are exactly R\Q, so all real numbers which are not rational, so for example the complex number i would not be irrational, but not rational either.
I have a proof for the converse of statement in the thumbnail but the comment character limit is too small for my proof
Just watch this impressive Math channel czcams.com/channels/ZDkxpcvd-T1uR65Feuj5Yg.html
Lmao
Fermat primes are of the format 2^n + 1. The first non prime of the format 2^n - 1 is 15 = 3 * 5 = 2^4 -1.
Would you call √(-1) irrational?
I guess I always thought of irrational numbers as being the real numbers minus the rational numbers, not just anything outside the set of rational numbers.
I wonder if that's standard or just my own particularity (or even mistake!).
This occurred to me in the first list of pairs of statements being evaluated as true or false. Sure,
√2 is irrational
and
√2 is not in the set of rational numbers
are both true.
But it occurred to me that these might not strictly be the same claim.
Thoughts?
I remember in school we learned that anything that can’t be written in the form Q/P where Q and P are integers and P doesn’t equal 0 is an irrational number. I don’t think complex numbers can be written like that. Bug then again that might just be a definition given to kids who couldn’t understand anything more complex.
You are a genuine mathematician.
I have a question. Take the statement P: If x is a real number then x
False, because the if part says that x is real and that implies x maybe is 6
you obviusly know that 6>0
For the last statement around 3:00 to be true, one must understand "differentiable" to mean "differentiable everywhere".
I usually like to attempt these problems, often by only looking at the thumbnail and without starting the video. When I saw this thumbnail my only reaction was good grief and only in seven minutes.
Good teacher
Please include this in one of your videos,
Solve for x,y,z in the interval [4,40] such that
x+y+z=62
xyz=2880
4;18;40
Hey micheal please make videos on advance group theory, it will be a great help
Just watch this impressive Math channel czcams.com/channels/ZDkxpcvd-T1uR65Feuj5Yg.html
Could you please post a video explaining any mathematical proof with details of mathematical statements and how they come?!
nice video
8-6÷2×3=?
Скобки раставь
А то здесь получается либо 6/(2×3), либо (6/2)×3.
@@user-gg5bl4ph6v =-1
@@Mathcambo, или 7?
Данное выражение не одназночно
"all real numbers are not rational"... it's interesting how you phrase that. it's like... (all real numbers) } rational, but the sentence most commonly reads as "all x in real numbers are not rational", which is most definitely false. strange
Good place to stop? You havn't finished warming up. I was expecting a bit more.
That would be a good place to START, in my opinion :)
P(x): if an integer x ends in 0 it is divisible by 10... if you are working in base 10 😉
I think in other bases it works too. 100 in base two is equal to 8 in base ten. 10 in base two is equal to 2 in base ten. 8 is divisible by 2.
in base 3:
100 = 9 in base ten
10 = 3 in base ten
in base 16:
100 = 256 in base ten
10 = 16 in base ten
I think no matter what number bases you're on, 100 is divisible by 10. cmiiw.
@@cepatwaras Supous you are on base k (k€N) then 10 in base k is 1*k+0=k, in the other hand if a number which ends in 0, lets call it abc...yz0 (the letters are the digits) and lets supuose it has n digits, in base ten that number is a*k^(n-1)+b*k(n-2)+...+z*k so you can factor a k subtracting one from each of the exponents.
Finally cause you prove that, with the two numbers in base 10, one is a multiple of the other. Then it has to be multiple in base k aswell because the base of a number does not matter with their multiples.
@@cepatwaras Sorry if there are any misakes I'm from Spain and here it is nearly 2 AM im tired.
Yes, it's true, for example 256 in base 16 is 100, ends in 0 and is not divisible by 10
@@ibrahimmassy2753 But when you write the value 256 as "100" in base sixteen, then wouldn't it mean the divisor written as "10" should also in the same base sixteen (to which the value is 16)?
Therefore, 100 divided by 10 in base ten is equivalent to "100" divided by "10" in base sixteen, not "100" (base sixteen) divided by 10 (base ten).
I think it's confusing when you write a mathematical sentence where a number is written on some base and another number on some other base and then you do mathematical operation on those numbers. 🙏🏼
0 in not natural
Depends on the context
@@jomama3465 you better revise the chapter. 0 is uniquely defined as the only whole number that is not natural
@@chessematics ugh it depends in the context and you can't do anything about it. Just accept it
@@angelmendez-rivera351 well, not so what you think about me... Kindly explain that, i will like to correct myself
fI R sT
ooh are we gonna be seeing truth tables in a future video?
Just watch this impressive Math channel czcams.com/channels/ZDkxpcvd-T1uR65Feuj5Yg.html
I hope so