Dr. Trefor Bazett
Dr. Trefor Bazett
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The reason you should shuffle 7 times
Keep exploring at ► brilliant.org/TreforBazett to get started for free for 30 days, and to get 20% off an annual premium subscription!
References:
Key paper, Bayer & Diaconis: www.stat.berkeley.edu/~aldous/157/Papers/bayer_diaconis.pdf
Diaconis on @numberphile: ua-cam.com/video/AxJubaijQbI/v-deo.html
I also enjoyed a write up of the Bayer & Diaconis paper in Francis Su's Mathematics for Human Flourishing
0:00 The Shuffling Problem
2:18 The minimum number of shuffles
8:00 Gilbert Shannon Reeds Model
10:30 Computing Probabilities
15:52 Total Variation Distance
18:09 Brilliant.org/TreforBazett
Check out my MATH MERCH line in collaboration with Beautiful Equations
►beautifulequations.net/pages/trefor
COURSE PLAYLISTS:
►DISCRETE MATH: ua-cam.com/play/PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS.html
►LINEAR ALGEBRA: ua-cam.com/play/PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6.html
►CALCULUS I: ua-cam.com/play/PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m.html
► CALCULUS II: ua-cam.com/play/PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n.html
►MULTIVARIABLE CALCULUS (Calc III): ua-cam.com/play/PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd.html
►VECTOR CALCULUS (Calc IV) ua-cam.com/play/PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa.html
►DIFFERENTIAL EQUATIONS: ua-cam.com/play/PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw.html
►LAPLACE TRANSFORM: ua-cam.com/play/PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1.html
►GAME THEORY: ua-cam.com/play/PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlX.html
OTHER PLAYLISTS:
► Learning Math Series
ua-cam.com/video/LPH2lqis3D0/v-deo.html
►Cool Math Series:
ua-cam.com/play/PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho.html
BECOME A MEMBER:
►Join: ua-cam.com/channels/9rTsvTxJnx1DNrDA3Rqa6A.htmljoin
MATH BOOKS I LOVE (affilliate link):
► www.amazon.com/shop/treforbazett
SOCIALS:
►X/Twitter: X.com/treforbazett
►TikTok: tiktok.com/@drtrefor
►Instagram (photography based): treforphotography
Переглядів: 55 268

Відео

Could 1-1+1-1+1-1+1-1+... actually converge?
Переглядів 64 тис.2 місяці тому
Keep exploring at ► brilliant.org/TreforBazett. Get started for free for 30 days - and the first 200 people get 20% off an annual premium subscription! A series convergence in the normal sense when the limit of partial sums converge. We will commonly say the geometric series converges and the harmonic series diverges because their partial sums do. But Cesàro Summation instead considers the aver...
Why don't whales get more cancer? - Peto's Paradox
Переглядів 10 тис.5 місяців тому
Keep exploring at ► brilliant.org/TreforBazett. Get started for free for 30 days - and the first 200 people get 20% off an annual premium subscription! 1st cited paper showing the algebraic model for estimating cancer probabilities by Calabrese and Shibata: bmccancer.biomedcentral.com/articles/10.1186/1471-2407-10-3 2nd cited paper focusing on whales by Caulin et al: royalsocietypublishing.org/...
How to write your homework using LaTeX
Переглядів 109 тис.5 місяців тому
Get the (free) Homework Template ► www.overleaf.com/read/pycnqvvptsvf#94a8a3. This template is on Overleaf, my thanks to Overleaf for sponsoring today's video. Overleaf is a cloud-based LaTeX editor that makes it particularly easy (and free!) to get started learning LaTeX. The LaTeX full playlist ► ua-cam.com/play/PLHXZ9OQGMqxcWWkx2DMnQmj5os2X5ZR73.html 0:00 Intro to LaTeX 1:14 Getting started ...
How to fairly split weird bills using GAME THEORY
Переглядів 124 тис.5 місяців тому
Keep exploring at ► brilliant.org/TreforBazett. Get started for free for 30 days - and the first 200 people get 20% off an annual premium subscription! 0:00 The Taxi Problem 4:27 Cooperative Game Theory 6:49 Shapley Value 8:08 Computing Chapley Value 10:11 The axiomatic approach 14:01 An alternate perspective 15:31 brilliant.org/TreforBazett Check out my MATH MERCH line in collaboration with Be...
Why hyperbolic functions are actually really nice
Переглядів 119 тис.6 місяців тому
Keep exploring at ► brilliant.org/TreforBazett. Get started for free for 30 days - and the first 200 people get 20% off an annual premium subscription! Today we unpack everything to do with hyperbolic functions. In calculus we often see an analytic definition of hyperbolic cosine and hyperbolic sin expressed as exponential functions. But why? Analytically, this is just asking for the even and o...
Modelling with Differential Equations // Lanchester Square Collapse
Переглядів 9 тис.6 місяців тому
Create interactive math documents with MAPLE LEARN: www.maplesoft.com/products/learn/?p=TC-9857. Thank you to MapleSoft for sponsoring today's video. In this video we use mathematics to model war. We will see a system of differential equations that leads to something called Lanchester Square Model and helps explain the phenomenon of Lanchester Square Collapse, where wo armies that were original...
5 counterexamples every calculus student should know
Переглядів 97 тис.7 місяців тому
You can play around with these counterexamples in this MAPLE LEARN document: learn.maplesoft.com/d/AGHGFLKNBGCIBKFRGUHLPHNPBIBLMKFOKSHNFNGSDOIKNNOSCKEGOJNICTDNEOLNKOGHNPHOLTAPOLNNAJDPCFNLASDFFSISMHMN My thanks to Maple Learn for sponsoring today's video. Claim 1: Discontinuities are isolated Counterexample: The dirichlet function (1 for rationals, 0 for irrationals) is discontinuous everywhere ...
My favorite way to compute Pi....experimentally!
Переглядів 12 тис.8 місяців тому
Check out more pi approximation in this Maple Learn document: learn.maplesoft.com/d/OLPIBQFTPFEFGIJUKMLJAGDSARFQOTDGHHKIPUDIAFPGJHCQJULLHQMPJSLTIIPFGGMFNIEUGHCSFMEOIUBJJHFOJPMGBQDUHJEL My thanks to @maplesoft for sponsoring today's video! Buffon's problem is an experimental way to compute pi. Drop a bunch of toothpicks on a paper with equally spaced lines. Then pi is nothing but 2 divided by th...
Why complete chaos is impossible || Ramsey Theory
Переглядів 38 тис.8 місяців тому
Keep exploring at ► brilliant.org/TreforBazett. Get started for free for 30 days - and the first 200 people get 20% off an annual premium subscription! Normal tic-tac-toe can always be drawn. But what if it lives in high dimensions? It turns out that no matter how large a tic-tac-toe board you have or how many players want to play, there always is a dimension long enough that guarantees the 1st...
The Math of Bubbles // Minimal Surfaces & the Calculus of Variations #SoME3
Переглядів 67 тис.9 місяців тому
This is my entry to the #SoME3 competition run by @3blue1brown and @LeiosLabs. Use the hashtag to check out the many other great entries! 0:00 Fun with bubbles! 0:46 Minimal Surfaces 2:35 Calculus of Variations 6:27 Derivation of Euler-Lagrange Equation 11:31 The Euler-Lagrange Equation 13:10 Deriving the Catenoid 15:25 Boundary Conditions Bubbles naturally try to minimize surface area, and so ...
Weird Topological Spaces // Connected vs Path Connected vs Simply Connected
Переглядів 14 тис.9 місяців тому
Keep learning at ► brilliant.org/TreforBazett. Get started for free for 30 days - and the first 200 people get 20% off an annual premium subscription! What exactly does it mean for a space to be connected? In this video we will contrast the notions of connected, path connected and simply connected for a range of topological spaces such as the topologists sine curve, the torus, and the fascinati...
Solving the Gaussian Integral the cool way
Переглядів 37 тис.10 місяців тому
Check out MAPLE LEARN ►www.maplesoft.com/products/learn/?p=TC-9857. Try out the limited trial version of Maple Learn (for free) and start solving! My thanks to @maplesoft for sponsoring today's video. My video on the "normal" way to solve the Gaussian Integral using a double integral in polar coordinates ►ua-cam.com/video/mrcRODAx-Vk/v-deo.html&ab_channel=Dr.TreforBazett In this video we're goi...
Why this pattern shows up everywhere in nature || Voronoi Cell Pattern
Переглядів 130 тис.10 місяців тому
Keep exploring at ► brilliant.org/TreforBazett. Get started for free for 30 days - and the first 200 people get 20% off an annual premium subscription! 0:00 Voronoi Patterns in nature 0:53 Crystallization 3:03 Proving Cholera is waterborne 4:10 Greatest Circle Problem 6:21 The Kolmogorov-Avrami model 13:30 Brilliant.org/TreforBazett Voronoi cell patterns are ubiquitous in nature with many appli...
The Dirichlet Integral is destroyed by Feynman's Trick
Переглядів 139 тис.11 місяців тому
The Dirichlet Integral is destroyed by Feynman's Trick
Unlocking the secrets of Magic Square puzzles
Переглядів 28 тис.11 місяців тому
Unlocking the secrets of Magic Square puzzles
How to write a STEM paper
Переглядів 15 тис.11 місяців тому
How to write a STEM paper
The Fastest Multiplication Algorithm
Переглядів 94 тис.Рік тому
The Fastest Multiplication Algorithm
How to make your LaTeX documents BEAUTIFUL // LaTeX Tutorial
Переглядів 76 тис.Рік тому
How to make your LaTeX documents BEAUTIFUL // LaTeX Tutorial
YouTuber VS Professor
Переглядів 11 тис.Рік тому
UA-camr VS Professor
The Beauty of Symmetry: An Introduction to the Wallpaper Group
Переглядів 18 тис.Рік тому
The Beauty of Symmetry: An Introduction to the Wallpaper Group
The Bernoulli Integral is ridiculous
Переглядів 638 тис.Рік тому
The Bernoulli Integral is ridiculous
Intro to Gradient Descent || Optimizing High-Dimensional Equations
Переглядів 58 тис.Рік тому
Intro to Gradient Descent || Optimizing High-Dimensional Equations
My favorite LaTeX Tricks to save time
Переглядів 60 тис.Рік тому
My favorite LaTeX Tricks to save time
The fastest matrix multiplication algorithm
Переглядів 279 тис.Рік тому
The fastest matrix multiplication algorithm
Fractal Snowflakes, Symmetries, and Beautiful Math Decorations
Переглядів 8 тис.Рік тому
Fractal Snowflakes, Symmetries, and Beautiful Math Decorations
Topology is weird: The Ham Sandwich Theorem
Переглядів 45 тис.Рік тому
Topology is weird: The Ham Sandwich Theorem
Tricky logarithmic differentiation example
Переглядів 33 тис.Рік тому
Tricky logarithmic differentiation example
Tables in LaTeX || Full Tutorial || Intro to LaTeX Episode 8
Переглядів 77 тис.Рік тому
Tables in LaTeX || Full Tutorial || Intro to LaTeX Episode 8
The Reciprocal Prime Series (this proof should be taught in calculus!)
Переглядів 109 тис.Рік тому
The Reciprocal Prime Series (this proof should be taught in calculus!)

КОМЕНТАРІ

  • @snblzd
    @snblzd 6 годин тому

    you are the best teacher on UA-cam

  • @culturecreating
    @culturecreating 8 годин тому

    @5:53 how to prove that its indeed a normal? anyone with the short answer.

    • @culturecreating
      @culturecreating 8 годин тому

      there is already few comments on this, thanks

  • @varathannk264
    @varathannk264 8 годин тому

    Thank you so much sir

  • @maximuz8533
    @maximuz8533 19 годин тому

    2 days of my life explained in 1 video

  • @hobosbro5863
    @hobosbro5863 19 годин тому

    Ok. Hear me me out. You know the parenthesis has to equal 3. So you replace it with X so the equation is 6/2x=9. Once you solve for x the answer is X=27. If you have 6/2x=1 you get X=3. Therefore the correct answer has to be 1.

  • @user-hf3rr5ir7r
    @user-hf3rr5ir7r 21 годину тому

    Hiii sir if file delete on latex how to recover please tell me

  • @TromCrabst
    @TromCrabst 23 години тому

    I love how the deeper we go, the more wild his hair gets. I can't wait to see how it looks by the end of the course

  • @TromCrabst
    @TromCrabst День тому

    Wait, "~" is spelled "knot"? I assumed it was just "not" since it kind of means the same thing haha

  • @borissimovic441
    @borissimovic441 День тому

    Can someone please explain, if you can how the length of a vector, which is 1D “a line” (length of cross product vector) can be equal to the area which is 2D (2d space includes more information width and length) for example something has a length of 10cm, not 10cm2, how can length be expressed in area terms since the length is 1D and area is 2D?

  • @borissimovic441
    @borissimovic441 День тому

    Can someone please explain, if you can how the length of a vector, which is 1D “a line” (length of cross product vector) can be equal to the area which is 2D (2d space includes more information width and length) for example something has a length of 10cm not 10cm2, how can length be expressed in area terms aisnce length is 1D and area is 2D?

  • @ArnoHill
    @ArnoHill День тому

    The total for the green column should have been 33 and not 23. If corrected Dr. Trefor would have gotten (12+13+13+25+12=75 ) / (25+27+33+45+25=155 ) =75/155 =0,4839 Intersect / Total

  • @jacksmith6972
    @jacksmith6972 День тому

    imma bout to do a brain bending move: graham(tree(graham(65)) ⬆⬆⬆⬆⬆ graham(tree(graham(65))

  • @arthurzindel9547
    @arthurzindel9547 День тому

    why is g = 0 in the definition? The constrain said y^2+x^2 = 1 and I don't understand where that 0 came from, is it a definition?

  • @Amaru1111
    @Amaru1111 День тому

    Kind of complicated but i think solving some examples will get me grasp it more

  • @hugoelmhall6673
    @hugoelmhall6673 День тому

    Great video, but is he trying to talk as fast as humanly possibly? Had to play it in 0.9x speed

  • @borissimovic441
    @borissimovic441 День тому

    Can someone please explain how can the length of a vector (cross product) which is a “1D line” be equal to the area which is 2D this is somehow confusing to me?

  • @mauriciobenjaminmossi8231
    @mauriciobenjaminmossi8231 День тому

    For \Sigma sqrt(n^3+n)/(n^4-n^2) is the following a valid test for divergence / convergence: sqrt(n^3+n)/(n^4-n^2) < n^2/(n^4-n^2) < n^2/(n^2(n^2-1)) < 1/(n^2-1) < 1/n^2, and in the limit 1/n^2 tends to zero.

  • @mauriciobenjaminmossi8231
    @mauriciobenjaminmossi8231 День тому

    You could also apply PFD (partial fractions) and then perform the integral test.

  • @shaunpatrick8345
    @shaunpatrick8345 2 дні тому

    You say it's ambiguous, essentially because people have not been taught what juxtaposition is and where it comes in the accepted order of operations. You suggest using brackets to remove ambiguity. OK, I've not been taught what brackets mean, so it's still ambiguous. Your move.

    • @RS-fg5mf
      @RS-fg5mf День тому

      You've had a poor education if you haven't been taught the purpose of parentheses/brackets/braces. Fyi... Parenthetical Implicit Multiplication does not have priority over Division and this guy is wrong... The expression is not ambiguous when you actually understand and apply the Order of Operations and the various properties and axioms of math correctly as intended.... The correct answer is 9

  • @chewoods6583
    @chewoods6583 2 дні тому

    You are a complete waste of time. Thank you for wasting my time.

  • @divyanshipandey4580
    @divyanshipandey4580 2 дні тому

    thank you so much ... i was so worried that how will i pass this exam... but your videos are seriously helping me to understand the topics clearly ... THANK YOU

  • @advancedappliedandpuremath
    @advancedappliedandpuremath 2 дні тому

    Hi Sir how can we find the null space of set of vectors from M2x2

  • @orwelliannonsense6566
    @orwelliannonsense6566 2 дні тому

    Thank you for this wonderful video which gives a summary of convergence test techniques. I also like the energy I feel when I watch your videos.

  • @riverevr6891
    @riverevr6891 2 дні тому

    This is very clear and concise, however, I want to know why we're doing these things. I am given the impression that this is just something to be remembered for different cases, which I don't particularly like as these things are often forgotten with some time.

  • @masoomparwej5650
    @masoomparwej5650 2 дні тому

    Hlo.. Plz suggest book for vector calculus for understanding these concepts

  • @adarshyadav1339
    @adarshyadav1339 2 дні тому

    Superb best explanation!! thanks for it

  • @emmvee2932
    @emmvee2932 2 дні тому

    I don't comprehend the ambiguity comment one bit although I do get it is ambiguous as to what answer the creator of the equation wanted. As far as I know math only ever has 1 correct answer. You do brackets 1st. Here is solving without using bedmas: 6/2(1+2), to: 3 (1+2), to: 3(3) = 9. The problem seems to be that people think they are using bedmas because they do the addition 1st but they are really not. The 1st step is to remove the brackets and that means doing the math inside the bracket and then doing the multiplication of the bracket itself 1st. ex: 6/2(1+2), to: 6/2(3), to: 6/6. Is there not a difference between these 2 formulas: 6/2x3 vs 6/2(3)?

    • @RS-fg5mf
      @RS-fg5mf День тому

      No, there is no mathematical difference between 6÷2×3 and 6÷2(3) despite the false and misleading information and subjective opinions people have about parenthetical implicit multiplication... Parentheses group and give priority to operations WITHIN the symbol of INCLUSION not outside the symbol. Parentheses also serve to delimit the TERM outside the parentheses from the TERM or TERMS within the parenthetical sub-expression... Keeping the parentheses at that point 6÷2(3) can only serve to let you know that the value of 3 came from a parenthetical sub-expression... When there are no OPERATIONS left INSIDE the parentheses to evaluate you can remove the parentheses and replace with an explicit multiplication symbol or leave them to represent implicit multiplication which is simply multiplication without the need for a physical multiplication sign... There is no rule in math that says you have to open, clear, remove, take off, eliminate or get rid of parentheses. The RULE is to evaluate operations WITHIN the symbol of INCLUSION as a priority and nothing more.... The correct answer is 9

    • @emmvee2932
      @emmvee2932 22 години тому

      @@RS-fg5mf the funny part is people actually think they are using bedmas and get 9. Check this out, I will solve it doing the unarguable 1st step unarguably as the very last step: 6/2(1+2), to 3(1+2), to (3 x 1) + (3 x 2), to 3+6 = 9.

    • @emmvee2932
      @emmvee2932 21 годину тому

      @@RS-fg5mf "There is no rule in math that says you have to open, clear, remove, take off, eliminate or get rid of parentheses. The RULE is to evaluate operations WITHIN the symbol of INCLUSION as a priority and nothing more". I'll *pretend* that is correct and that the math inside brackets is done 1st without clearing the brackets. Solve this for Y: Z= 3(1x+2y). I'd love to see you complete only the very 1st step as you claim it is done. Please solve what's inside the bracket you know without multiplying it by the number outside of the bracket (i.e. 3) 1st. Show your work.

    • @RS-fg5mf
      @RS-fg5mf 19 годин тому

      @@emmvee2932 you CAN'T SOLVE z=3(1x+2y) you can simplify 3(1x+2y) to equal 3x+6y that doesn't mean you're required to remove the parentheses... Although keeping them at that point is redundant... You can also rewrite the equation z=3(1x+2y) as z/3 = 1x+2y OR z/(1x+2y)= 3 But you CAN'T solve the equation as written.. Let me be even more succinct... The Distributive Property is NOT required if what is inside the parentheses can be FULLY evaluated and SIMPLIFIED... You can always choose to Distribute even when the contents of the parentheses can be FULLY evaluated and SIMPLIFIED but there is no RULE in math that says you have to.... While the intended purpose of the Distributive Property is to eliminate the NEED for parentheses that doesn't mean that removing parentheses is a requirement... For example... 6÷2(1+2)= 6÷2(1)+6÷2(2) OR 6÷2×1+6÷2×2 ... With or Without the parentheses... 6÷2(a+b)= 9 3(a+b)= 9 a+b=9÷3 a+b=3 3-b=a 3-a= b That's ALL that can be done with that .... 6÷2(y+2)= 9 3(y+2)=9 y+2=9÷3 y+2=3 3-2=y y=1 6÷y(1+2)=9 6÷y(3)=9 6÷y=9÷3 6÷y=3 6÷3=y y=2 y÷2(1+2)=9 y÷2(3)=9 y÷2=9÷3 y÷2=3 2×3=y y= 6 THAT'S how Algebra works...

  • @user-pb6zg6vw3w
    @user-pb6zg6vw3w 2 дні тому

    Does the Laplace Transform work for the solution of non-CCL ODEs?

  • @damirvukelic8087
    @damirvukelic8087 2 дні тому

    The answers is quite easy: you earn 6 dollars a day. You spend 50% on food and the rest you multiply by 3 by winning at say car racing betting. 6/2x3=9

  • @IoannisPap_
    @IoannisPap_ 2 дні тому

    Maybe I misunderstood something but: if your function was R-linear, i.e. f(cx)=cf(x) for all real x and c, then f would be onto. This is a contradiction since f(R)=Q. What do I miss? If I'm not wrong what you say is that R is a Q-vector space, and f is a Q-linear map. The map you described is not R-linear. I wonder if there is a discontinuous additive real function f, such that f(cx)=cf(x) for all real x,c

  • @lazik711
    @lazik711 3 дні тому

    On the board or in the book, I agree. When programming, it comes out 9 - c language, python, fortran, octave, libreoffice...

  • @carlossegura403
    @carlossegura403 3 дні тому

    Frequentist probability is based on the long-run frequency of events observed in repeated trials. In contrast, Bayesian probability represents a subjective degree of belief, incorporating prior information and updating with new data.

  • @RAMKUMAR-rh4um
    @RAMKUMAR-rh4um 3 дні тому

    Nice T shirt sir, covered all functions 😊

  • @monkeydog8681
    @monkeydog8681 3 дні тому

    Honestly. Those super colossal numbers are so ridiculous, infinity is easier to understand.

  • @purushottamsahu4306
    @purushottamsahu4306 3 дні тому

    Can we get the pdf of slides which you use?

  • @user-wp2pl8dx6s
    @user-wp2pl8dx6s 3 дні тому

    I love it so much! Can you share which software you use to draw these pictures?

  • @willardsavage2980
    @willardsavage2980 3 дні тому

    why you didnt make the limits of integration you confused me, cuz the limits of integration in my opinion are radius 1, and angle 2pi, but since you did that thing of pi*rsquare, i didnt get what you did so i dont know if i did wrong or well, why im gettin 4 pi in the final answer i dont understand can you explain this please, i get that you use the formula of the area, but i wanna know how to do it with limits of integration, since limits of integration is what i will need to use in the exam, not a formula of an area, thank you

  • @rmhartman
    @rmhartman 3 дні тому

    ... or you could just use RPN notation ...

  • @rmhartman
    @rmhartman 3 дні тому

    "resolving the parens" means resolving what is _inside_ the parens. Once that is done, the parens go away. a number next to a paren is an implied multiplication, and it would be clearer if it was written with an explicit multiplication operator there ... but it does not alter the precedence. After resolving the "(2+1) what you have left there is 3. so 6 ÷ 2 * 3, which are taken left to right. And you do everyone a disservice in your argument by putting parens which were never there around the 6 ÷ 2. It confuses people, who ask "why did you put parens there when they never were there to begin with". You don't need them.

  • @user-sm4sf4ff2i
    @user-sm4sf4ff2i 3 дні тому

    Cheer~~~act dishonestly or unfairly in order to gain an advantage, especially in a game or examination.😊

  • @MatEma-11235
    @MatEma-11235 3 дні тому

    why is it like pi over four?

  • @morrismanganhe1113
    @morrismanganhe1113 3 дні тому

    💯

  • @FilthyHedgeHog
    @FilthyHedgeHog 3 дні тому

    ء itemع

  • @sfundomsezane
    @sfundomsezane 3 дні тому

    In calculus 1, it is stated that a function is a one-to-one function if the vertical line test intersects the function at most once. How does this change when dealing with multivariable functions?

  • @baxtermullins1842
    @baxtermullins1842 3 дні тому

    In order to avoid confusion, I require parentheses, brackets and Braces to be used. Then, (6 -. 2)(1+2) or 6-.[2(1+2)]. Note divide is -. Due to lack of symbols. So, end the confusion!

    • @GanonTEK
      @GanonTEK 3 дні тому

      100%

    • @RS-fg5mf
      @RS-fg5mf 22 години тому

      What you require and what is actually a requirement are two different things... 6÷2(1+2)=9 no extra parentheses required 6÷(2(1+2))=1 two sets of grouping symbols required.

  • @triteraerlangga7917
    @triteraerlangga7917 4 дні тому

    So g(TREE(3)) Would surely bigger than TREE(3)?

  • @nikolaslouka3878
    @nikolaslouka3878 4 дні тому

    εχεις τεραστια αρχιδια

  • @ryanlak139
    @ryanlak139 4 дні тому

    For Tree(3), could you not just add an infinte amount of 'yellow' nodes to a 'green' node? How then is the number finite?

  • @zaccalvert7341
    @zaccalvert7341 4 дні тому

    Why didn't I find you earlier?! Great clear explanations.

  • @dayssalmon-te6430
    @dayssalmon-te6430 4 дні тому

    This is seriously one of the best structured math videos Ive seen, so damn useful. Well done!