*_Ayooooooooooooooooo! :D Liked what you saw? If so, please sub and support the channel with deez:_* Train your Number Theory Expertise by trying out Brilliant! =D brilliant.org/FlammableMaths Check out my newest video over on @Flammy's Wood ! =D ua-cam.com/video/07RavF0J24I/v-deo.html Support the channel by checking out Deez Nutz over on stemerch.eu/products/deez-nuts-premium-3d-cutting-board?_pos=1&_sid=3ebd4ef06&_ss=r ! :3 Engi Watch: stemerch.com/products/the-incredibly-unrigorous-engineering-watch?variant=40377075728562
@@ginalley ³ you mean that? The German keyboard has ² and ³ bound to a key combination, and on mobile many keyboard apps can do ⁰¹²³⁴⁵⁶⁷⁸⁹ⁿ. Or you copy the unicode symbol from one of the many websites. Using that you can also do ₀₁₂₃₄₅₆₇₈₉ₓ btw. I find that very ⁿⁱᶜᵉ.
10:14 wtf was Papa thinking here. -3 >= y >= 0 implies -3 >= 0, a contradiction. In fact if you do it the correct way you do get -3 = 0 and -3 = y and the y
Either I'm stupid or there's a mistake around 10:20 because you wrote -3>=y and then wrote that -1 is a solution for y. So -3>=-1? Same for -2. Actually I think i found the mistake, you divided by y which is negative so the relation should have been flipped right?
You have to accept the result knowing that if you think he is wrong is you that can't understand: God Flammy never makes mistakes and acts from a higher dimension of intelligence and consciousness🙏
@@trillionman2105 i really didn't understand what you wrote about. I just try doing a bit of "research" before saying that someone else is wrong. Nobody is perfect, including me. If I see something wrong, it's my responsibility to ascertain that it is definitely wrong before acting on it.
The inequality is wrong, it should be y greater or equal to negative 3 but less than 0 because if y less than -3, we see that y(y+3) is a positive integer.
9:41 You can't divide by y in an inequality because you don't know whether y is positive or negative lol, just use the "Wavy Curve Method"/"Interval Method" or whatever else it's called and you'll get 0>=y>=-3
I recommend your channel to anyone who wants a in depth guide in how to think about math. It seems to me that we're taught (USA) to think of math as esoteric and you have to have tips and tricks to solve problems. After i watch one of your videos, it always makes me want to think of ways i can tackle problems rather than try to smash my brain into the page and hope i come away with anything. Thanks, greatly appreciated.
-27+19=-8, and the cuberoot of -8 is not solvable in the integers 12:43 (I was incorrect, even by evaluating the complex roots, you get a real solution of -2. he still evaluated the wrong root though)
No, the cube root of -8 is solvable in the integers. As an odd root of a negative number, the principle root is negative (so obviously real), and in this case is also an integer.
*_Ayooooooooooooooooo! :D Liked what you saw? If so, please sub and support the channel with deez:_*
Train your Number Theory Expertise by trying out Brilliant! =D brilliant.org/FlammableMaths
Check out my newest video over on @Flammy's Wood ! =D ua-cam.com/video/07RavF0J24I/v-deo.html
Support the channel by checking out Deez Nutz over on stemerch.eu/products/deez-nuts-premium-3d-cutting-board?_pos=1&_sid=3ebd4ef06&_ss=r ! :3
Engi Watch: stemerch.com/products/the-incredibly-unrigorous-engineering-watch?variant=40377075728562
More resources for olympiad preparation 👍
I will watch your other channel as soon as my exams are over
You know I love my Papa Flammy! Can't wait for my incredibly unrigorous engineering watch to arrive!
9:40 if we divide by y, we still have to respect the sign of y, because if y= changes to 0>=y+3 - this one is contradiction.
So, finally, -3
Aah. The sign. I was so hung on this inequality until I read your comment. Thanks.
12:51 Small error. Should be -27+19=-8, then -2 for the root.
-27+18+1=-1×S(7) So then if x³=-8 then cuberoot of -8 is -2 and yes, (-2,-3) is an answer.
Oh, yes, obviously! Sry for the confusion and thx for pointing it out! =)
@@RockHardWoodDaddy you pulled out your wood on your main channel?? damn....
@@livedandletdie how did you manage to do x^3 properly in the comments
@@ginalley ³ you mean that? The German keyboard has ² and ³ bound to a key combination, and on mobile many keyboard apps can do ⁰¹²³⁴⁵⁶⁷⁸⁹ⁿ. Or you copy the unicode symbol from one of the many websites. Using that you can also do ₀₁₂₃₄₅₆₇₈₉ₓ btw. I find that very ⁿⁱᶜᵉ.
day 1 of asking papa flammy to make a complex differential geometry series
what even is that
@@faker530 it's differential geometry but with complex manifolds
I think that’s a little too advanced for this channel lol
day 1 of agreeing with this guy ^
10:14 wtf was Papa thinking here. -3 >= y >= 0 implies -3 >= 0, a contradiction.
In fact if you do it the correct way you do get -3 = 0 and -3 = y and the y
so he should have found the range graphically, and then with the solutions it should be x=-2 for y=-3
Either I'm stupid or there's a mistake around 10:20 because you wrote -3>=y and then wrote that -1 is a solution for y. So -3>=-1? Same for -2.
Actually I think i found the mistake, you divided by y which is negative so the relation should have been flipped right?
Yep. I was also confused about that. But there are certainly a lot of helpful commentators around :)
You have to accept the result knowing that if you think he is wrong is you that can't understand: God Flammy never makes mistakes and acts from a higher dimension of intelligence and consciousness🙏
@@trillionman2105 i really didn't understand what you wrote about. I just try doing a bit of "research" before saying that someone else is wrong. Nobody is perfect, including me. If I see something wrong, it's my responsibility to ascertain that it is definitely wrong before acting on it.
@@ADthehawkof course, I was just joking
The inequality is wrong, it should be y greater or equal to negative 3 but less than 0 because if y less than -3, we see that y(y+3) is a positive integer.
I believe the final pair is actually (-3, -2), since -27 + 18 = -8, not 8.
Define fk(n) to be the sum of all possible products of k distinct integers chosen from
the set {1, 2, . . . , n}, i.e.,
fk(n) = X
1≤i1
I love these videos of equations with eggs and wah
Seggs and wine
10:14
You forgot to take the modolus for it to be true.
in 10:28, i don't understand how y>=0, can anyone explain to me ? :D
just as an example :)
9:41 You can't divide by y in an inequality because you don't know whether y is positive or negative lol, just use the "Wavy Curve Method"/"Interval Method" or whatever else it's called and you'll get 0>=y>=-3
Greetings from Bulgaria and thank you!
Oh shit papa flammy made a mistake let’s all rollover and hara-kiri
Wow I am early. Love your content so much, been following this channel for years now and I won't stop as long as you don't!
-27+18+1=9.
-27+18+1=8
You fixed it and it was still wrong.
Can we solve it by algebra instead of inequality?
Lovely people bulgarian and German
I'm from bulgaria, the math here is one of the best in the world. I will greet you in Bulgarian-Здравейте, много си добър фламабъл мат, обичам те!!!❤
Few mistakes there
a uge thankyou to byyant
I don't like unnecessary talk in your video 🤦..
I love that a lot of these are from 1999, the year I was born :D
For y0 we have y^2+3y>0 => y^3
There should be a math/education youtuber boxing event
I want to see papa destroy andrew copeson
sorry papa, but -27 + 19 is equal to -8, you forget to add negatif sign lol
I recommend your channel to anyone who wants a in depth guide in how to think about math. It seems to me that we're taught (USA) to think of math as esoteric and you have to have tips and tricks to solve problems. After i watch one of your videos, it always makes me want to think of ways i can tackle problems rather than try to smash my brain into the page and hope i come away with anything. Thanks, greatly appreciated.
When you divide by a negative y, your inequality 0>= y(y+3) changes direction to 0
It might have been nice to talk about how this is an elliptic curve too!
Very interested in checking out your wood Papa Flammy.
This question is as stupid as I think I'm stupid
Thnk u
garfuekd
Papa I'm first
Hmmmm nice.
Papa bless me
Isn't it -8 and -2?
You would know if you watched the video
-27+19=-8, and the cuberoot of -8 is not solvable in the integers 12:43 (I was incorrect, even by evaluating the complex roots, you get a real solution of -2. he still evaluated the wrong root though)
You can't take the cuberoot of -8 directly, right. But nevertheless, the equation x³ = -8 has the solution x = -2.
@@bjornfeuerbacher5514 yes that was his reasoning though
@@kensmusic1134 Actually, he took the cuberoot of +8, since he made an error in the preceding calculation.
@@bjornfeuerbacher5514 yes, but with the correct calculation, this argument does not make sense, which was my point
No, the cube root of -8 is solvable in the integers. As an odd root of a negative number, the principle root is negative (so obviously real), and in this case is also an integer.
PLEASE write LARGER! Thanks 👍!!