Proof by Mathematical Induction (Precalculus - College Algebra 73)

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  • เผยแพร่เมื่อ 29 ต.ค. 2024

ความคิดเห็น • 179

  • @Vanzorz1
    @Vanzorz1 3 ปีที่แล้ว +269

    Yes! This is Amazing, incredibly useful for CS students, Please do consider a Discrete Mathematics series, it would help us a lot.

    • @PBDNR
      @PBDNR 3 ปีที่แล้ว +19

      yeah discrete was quite the class. a good series on it would be super helpful for lots of students.

    • @amitbhagat120
      @amitbhagat120 3 ปีที่แล้ว

      Hmmm

    • @donjuan6118
      @donjuan6118 3 ปีที่แล้ว

      Define "discrete". Because when you take (or anyone takes) Theory of Computation, it's all graph theory application to automata.

    • @marksolvent3259
      @marksolvent3259 3 ปีที่แล้ว +2

      Yeah that would help a lot. I like how this guy dumbs things tf down

    • @noelpadavan5674
      @noelpadavan5674 3 ปีที่แล้ว

      Agreed!

  • @autumrose8710
    @autumrose8710 2 ปีที่แล้ว +11

    This man is truly getting me through my degree. Thank you for all you do.

  • @gianlucamazzi7878
    @gianlucamazzi7878 3 ปีที่แล้ว +21

    Just wanted to leave a comment saying how amazing this guy is and he is the only reason I passed Calc 3. I had a teacher who wasn’t very good at teaching but professor Leonard helped me be one of the few that passed with a good grade

  • @marywangui4682
    @marywangui4682 3 ปีที่แล้ว +10

    You cannot imagine what it felt to come across this channel.. As an international student learning in a different language.. You are t God sent.. Just finished my calc 1 and passed.. I really appreciate..

  • @danielmadison4451
    @danielmadison4451 4 หลายเดือนก่อน +5

    I fear we have lost you sir. What a devastating loss. I hope you are well and I will always continue to look for your return. A long long time fan.

  • @name8166
    @name8166 3 ปีที่แล้ว +10

    Hey, please comeback professor. We seriously need you. Lectures on Trigonometry, Complex variables and Partial differential equations are needed. You are our only hope.

  • @georgesadler7830
    @georgesadler7830 2 ปีที่แล้ว +6

    Professor Leonard, thank you for a basic Introduction to Mathematical Induction. Learning Mathematical Induction is very helpful in Discrete Mathematics, Advanced Calculus, Number Theory, Linear Algebra and future course in Mathematics. Mathematical Induction helps students to write proofs in Advanced Mathematics. Mathematical Induction helps me to fully understand Advanced Calculus.

  • @nutsa2014sniffgluee
    @nutsa2014sniffgluee หลายเดือนก่อน

    you are everything i needed for my discrete mathematics course. immaculate explanation, humanly most explicit explanation and breakdown of each and every activity... best mathematician youtuber in history

  • @JustMoseyinAround
    @JustMoseyinAround 3 ปีที่แล้ว +6

    Superman never disappoints. Thank you sir.

  • @slickbonz
    @slickbonz 3 ปีที่แล้ว +11

    I love your Calculus series ( I've watched all of it). It is the reason I passed Calc I and II. I can't wait until you are back in a classroom in front of students again. I miss your sense of humor.

    • @vanshikarawat7328
      @vanshikarawat7328 3 ปีที่แล้ว

      If you have taken notes from these lectures can please share them with me my email id is rawatvanshika26@gmail.com

  • @skylerpretto1221
    @skylerpretto1221 3 ปีที่แล้ว +5

    Best explanation of mathematical induction EVER!

  • @tasfiaahsan6262
    @tasfiaahsan6262 3 ปีที่แล้ว +9

    Its 2 am at night
    And i.am.watching your video and doing maths..your are.just amazing professor... Thank you.so much❤️

  • @josephthecreator
    @josephthecreator 2 ปีที่แล้ว +1

    Professor Leonard is the TRUTH! Thank you as always.

  • @glitchpirate71
    @glitchpirate71 หลายเดือนก่อน

    One of the best and most in-depth explanations on this short topic. Prof. Leonard should do a video course on Mathematical Thinking.

  • @Edgar632172
    @Edgar632172 3 ปีที่แล้ว +3

    Professor Leonard I am a big fan of the work you are doing! Please consider making a series on content related to proofs. Such material is really scarce to come across on the web even to this day unfortunately. It's a shame too because proofs are the bread and butter of understanding mathematics at a deeper level. :(

  • @marianasapori4776
    @marianasapori4776 6 หลายเดือนก่อน

    the way you set everything up made it click in my brain.. thanks so much

  • @a7xfreak55
    @a7xfreak55 2 ปีที่แล้ว

    Saving my life once again. Using induction in my Bridge to advanced math class and linear algebra class. After this video I'm golden.

  • @thenkaliway85
    @thenkaliway85 3 ปีที่แล้ว +4

    Wooow I've been looking for Mathematical Induction... Please do lots and lots of videos on it

  • @charbilrom3153
    @charbilrom3153 3 ปีที่แล้ว +2

    I can't said anything. I will meet this guy in person . I downloaded his videos from Cal 1-3 and statistics. I will watch this video for life. Imagine studying in college without knowing the language of lectures(arabic). All I have to do is watching P. Leonard videos and come for quiz or exams laughing at my colleague. 1 million subscribers is not enough to give. I don't know how to thank you.🤝🙏

  • @zander008
    @zander008 7 หลายเดือนก่อน +1

    Yet again Professor Leonard makes something so approachable that zybooks made feel so convoluted. Watching these videos always makes me wish I had time/money to go after a math degree with Professor Leonard teaching the classes!

  • @qbtc
    @qbtc 11 หลายเดือนก่อน

    Crystal clear lecture. You are a gift to the math community.

  • @ojingaj30
    @ojingaj30 3 ปีที่แล้ว +10

    Professor L,
    I really hope you will go over Trigonometry after College Algebra.
    Thanks for all your hard work!!

  • @reginapulane838
    @reginapulane838 3 ปีที่แล้ว +3

    Thank you Prof.....you are a blessing to students ❤❤❤❤❤❤❤❤💃💃💃💃💃💃💃💃💃I thank you a lot Prof, I managed to get my Bachelor of Education degree via your videos

  • @Mark-vl3zm
    @Mark-vl3zm 3 ปีที่แล้ว +3

    Hey Professor!! As of writing this comment I have taken my final and passed Pre-Calculus!! I will be taking Calculus 1 for Winter Semester 2021! Thank you so much for these videos they truly did help alot especially with Distance Learning being a thing. I'll see you in your Calc 1 Playlist. Thanks again!!

  • @mohammedalsulaiman5903
    @mohammedalsulaiman5903 3 ปีที่แล้ว +3

    I love your lecture. I’m from Saudi. I studied statistics 101 so it was wonderful time I spent during watching your lectures that time.

  • @ecmrn
    @ecmrn 8 หลายเดือนก่อน

    This man gives the best explanations on TH-cam

  • @kickbackprogrammer2253
    @kickbackprogrammer2253 2 ปีที่แล้ว

    wow... Still coming through for me way after Calculus... You're really the MVP. Thank you for all your videos, please keep going on this discreet mathematics/number theory lessons!

  • @hamzasehavdic
    @hamzasehavdic ปีที่แล้ว

    Goodness Leonard, this felt like a watershed moment for me
    (and the previous Series/Sequence and Asymptote videos)
    I feel like I have a tangible grip harnessing infinity
    God bless you

  • @alexEMP1
    @alexEMP1 ปีที่แล้ว

    Best explanation I’ve found from dozens of other videos

  • @sunshineberry9829
    @sunshineberry9829 ปีที่แล้ว

    I just wanted to say thank you so much! you'er angel sent from Haven... I've never understood math faster than this.

  • @johannesnilsen1904
    @johannesnilsen1904 4 หลายเดือนก่อน

    THIS IS EXACTLY WHAT I NEEDED. GREAT EXPLANATION :)

  • @mattrhoades9487
    @mattrhoades9487 3 ปีที่แล้ว +1

    Another way to explain it would be subtract the series of n=k terms from the series of n=k+1 terms and the only thing standing is the k+1th term on the left hand side and the difference between the right hand side terms...simplify the right hand side and show the right hand side (differences) equals the k+1th term.

  • @tanmoy.mazumder
    @tanmoy.mazumder 3 ปีที่แล้ว +1

    so good to see you uploading continuously, professor.
    best wishes

  • @thomasplatt7329
    @thomasplatt7329 10 หลายเดือนก่อน

    its unbelievable how quickly my stress dissipates when I see Prof. Leonard has a video covering what I'm stuck on.

  • @samueldarenskiy6893
    @samueldarenskiy6893 ปีที่แล้ว

    I would start worshipping this dude if made a linear algebra and discrete math playlist

  • @kwabenatorson6248
    @kwabenatorson6248 2 ปีที่แล้ว

    U've made me understand the concept in fullest

  • @rafaelkacaribu2081
    @rafaelkacaribu2081 4 หลายเดือนก่อน

    Thank you so much Proffesor Leonard, finally now I understand the basic concept of this mathematical induction. I will retake exam discrete math and hope i can answer the questions. Thank you sir

  • @sonalfernando7042
    @sonalfernando7042 11 หลายเดือนก่อน +1

    Subscribed ,thank you for your support.

  • @Gamechanger-Hub
    @Gamechanger-Hub 8 หลายเดือนก่อน

    Your videos are having good effect on my colleagues and I, We thank you so much 👏. We consider if we can have a playlist on Abstract Algebra with subtitles: Mapping, Binary Operation, Relations, Mathematical Induction, Divisors, Irrational Numbers, Rational Numbers, Complex Numbers, Congruence Modulo N, Groups, Rings and Fields.🙏

  • @maxd3589
    @maxd3589 3 ปีที่แล้ว +1

    Trigonometry with you, prof Leonard, would be such a blessing. Sadly I must proceed and finish it alone. Guess I'll have to go back to it when you do it!

  • @JoshuaKipkoech-b5e
    @JoshuaKipkoech-b5e 27 วันที่ผ่านมา

    God bless you prof Leonard
    Gaining alot lately

  • @gainsborough25
    @gainsborough25 2 ปีที่แล้ว

    Love your videos, and have used them to help prepare me for teaching my own calculus class!
    I do want to mention that you want to be careful about assuming what you are trying to prove. For example, at 19:25 when you start setting 1+5+9+... + (4k-3) + [4(k+1)-3] equal to what you want it to be.
    Instead, best practice would be simply manipulating the first part of your equality until you get it to the point that it looks like what you want to prove. For me, I did it like the following:
    1+5+9+... + (4k-3) + [4(k+1)-3]
    = 2k^2 - k + 4(k+1) - 3
    = 2k^2 - k + 4k + 4 - 3
    = 2k^2 +4k + 2 - k + 2 - 3 (splitting up the +4 here into two instances of +2)
    = (2k^2 +4k + 2) - k - 1 (association property and also simplified 2 - 3 to be -1)
    = 2(k^2 + 2k +1) - k - 1 (factor out the 2 in the grouped terms)
    = 2(k+1)^2 - k - 1 (factored the grouped polynomial)
    = 2(k+1)^2 - (k+1) (factored out a negative in the non-grouped terms)
    and at this point we can conclude that
    1+5+9+... + (4k-3) + [4(k+1)-3] = 2(k+1)^2 - (k+1) by the transitive property, and have proved the theorem by induction.
    thanks again for all your videos, prof!

  • @mohamedhesham6008
    @mohamedhesham6008 2 ปีที่แล้ว

    You are just out of this world thank you so much for this great video

  • @VictorMilanov
    @VictorMilanov 2 ปีที่แล้ว

    best explanation i have found on this. thank you

  • @tambuwalmathsclass
    @tambuwalmathsclass 3 ปีที่แล้ว

    So great

  • @parsarahimnia5376
    @parsarahimnia5376 ปีที่แล้ว

    professor Leonard, you are an amazing man

  • @LostArkLover
    @LostArkLover 3 ปีที่แล้ว

    Happy New and much blessings upon you Sir and family, and Much much appreciation for your efforts

  • @dbum896
    @dbum896 2 ปีที่แล้ว

    Super concise and optimally explained, thank you!

  • @kylemunsami6039
    @kylemunsami6039 3 ปีที่แล้ว +2

    Good day Professor, It sometimes goes unnoticed when amazing people do amazing things. While this pandemic has caused all our lives to change, your videos became a source of inspiration to us all students. Not many can be as detailed in content and explain with such enthusiasm. Thank you for being the essential worker we needed by delivering excellence on absolutely every video uploaded. May your 2021 be im'PECC'able("see what i did there-HA HA HA"-Preofessor Leonard).

  • @camquilici5422
    @camquilici5422 3 ปีที่แล้ว +46

    Professor, can you please put a Linear Algebra series on your todo list?

    • @adamharoon6021
      @adamharoon6021 3 ปีที่แล้ว

      this would be something I would watch

    • @Peter_1986
      @Peter_1986 3 ปีที่แล้ว +7

      He has already confirmed in his video "Professor Leonard's Important Announcement 2019" that he will make Linear Algebra videos in the future.

    • @adamharoon6021
      @adamharoon6021 3 ปีที่แล้ว

      @@Peter_1986 oh sweet

    • @أميرالبلابل
      @أميرالبلابل 3 ปีที่แล้ว

      @@Peter_1986 amazing

    • @name8166
      @name8166 3 ปีที่แล้ว

      @@adamharoon6021 Try James Hamblin for linear algebra

  • @blockrock44
    @blockrock44 3 ปีที่แล้ว

    Thanks so much! I have an exam in Discrete Mathematics to take today, and I know this will be very important for it! Really glad you had a video on it, especially from just a few days ago!!
    Hope you are well as you can be!

  • @korneliusadam
    @korneliusadam 3 ปีที่แล้ว +1

    lectures about linear algebra would be great! many thanks for these lectures, appreciate much what you are doing and for free. everything is explained in a great manner. if the donation is possible I would be glad to support as much as I can. I am sure there are many who would support such a great job. there are many lectures and lecturers but this is far above them.

  • @JudithTennes-f6v
    @JudithTennes-f6v ปีที่แล้ว

    Well understood with good explanation

  • @joaquinbustos3069
    @joaquinbustos3069 ปีที่แล้ว

    youre the best math professor ever

  • @stevewest6133
    @stevewest6133 ปีที่แล้ว

    Great idea, giving a subsequent example after the base case. It drives home the point that the SUM OF the left side at the nth term = formula on the right side with n plugged in.
    For example at n=3, the correct workup is 1+3+5 = 3^2, its NOT 2(3)-1 = 3^2. That's obvious. But at n=1, students might not get the distinction since 2(1)-1 does equal 1^2..... wrong process leads them to a true statement and confusion.

  • @apeiros7999
    @apeiros7999 3 ปีที่แล้ว

    You give great lectures! I hope to one day make as good videos as yours. You are a great inspiration to young people such as myself.

  • @IEHD01
    @IEHD01 ปีที่แล้ว

    Wow you explain this so well compared to my teacher. Thank you

  • @jonathan1414
    @jonathan1414 8 วันที่ผ่านมา

    Yes I have a better understanding now.

  • @williammendez5209
    @williammendez5209 3 ปีที่แล้ว +1

    I really hope you'll someday do a series on tensor calculus and differential geometry.

    • @Czmlol
      @Czmlol 3 ปีที่แล้ว

      I doubt that it's his domain.

    • @dpmike32819
      @dpmike32819 2 ปีที่แล้ว

      @@Czmlol I bet it is!,,

  • @rmarani3530
    @rmarani3530 3 ปีที่แล้ว +2

    Thank you so much sir

  • @qwqwtry7027
    @qwqwtry7027 3 ปีที่แล้ว +5

    Holy hellllllll!!!!!!!! He finalllyyy did!!!!!!!

    • @reginapulane838
      @reginapulane838 3 ปีที่แล้ว

      Yes 💃💃💃💃💃💃💃💃💃💃💃💃💃💃💃💃💃💃💃💃💃💃💃💃

    • @mellima4226
      @mellima4226 3 ปีที่แล้ว

      Hahahh love your reaction.

  • @dutonic
    @dutonic ปีที่แล้ว

    Awesome and clear lecture

  • @Atrainn234
    @Atrainn234 2 ปีที่แล้ว

    Thank you

  • @janoycresva276
    @janoycresva276 3 ปีที่แล้ว +4

    I wonder when he'll finish his Differential Equations series and start his Linear Algebra vids 🧐

  • @MarcelloPalucci
    @MarcelloPalucci 7 วันที่ผ่านมา

    I love this man

  • @squpsqup2708
    @squpsqup2708 3 ปีที่แล้ว

    All support for that professor

  • @Polyrthyawhut
    @Polyrthyawhut 3 ปีที่แล้ว +1

    One of the best.

  • @DomnickK
    @DomnickK 3 ปีที่แล้ว +1

    Oh please, get to Trig soon!

  • @saltedavocado8006
    @saltedavocado8006 2 ปีที่แล้ว

    YOU TEACH BETTER THAN MY PROFESSOR!!!!!

  • @renefagermo
    @renefagermo 2 ปีที่แล้ว

    Thanks, L!

  • @ayushishrivastava150
    @ayushishrivastava150 3 ปีที่แล้ว

    Please start a complete course of modern algebra.

  • @UnathiGX
    @UnathiGX 3 ปีที่แล้ว

    This makes me happy!

  • @nigeladams8321
    @nigeladams8321 3 ปีที่แล้ว +1

    this helped a ton

  • @nerdymath89
    @nerdymath89 3 ปีที่แล้ว

    Sir you're the BEST!

  • @user-pq2qd1sd8m
    @user-pq2qd1sd8m 3 ปีที่แล้ว +4

    can you explain the strong mathematical induction, please 🙏?
    I didn't understand it 😭😭, and I have final exam after week in discreet mathematics😭😭

  • @Peter_1986
    @Peter_1986 2 ปีที่แล้ว

    5:33
    "4 does equal 4 - that is really kinda cool!"
    Haha!

  • @cricketlover1105
    @cricketlover1105 2 ปีที่แล้ว +1

    This is amazing vedio

  • @gauravbains8426
    @gauravbains8426 10 หลายเดือนก่อน

    Thank you bro!

  • @cardinalblues7121
    @cardinalblues7121 3 ปีที่แล้ว

    Thank you for the amazing video, it helps me a lot ,Mr Kent ,oh...Professor Leonard :D

  • @adrianloh6919
    @adrianloh6919 3 ปีที่แล้ว +1

    What if the central of domino not falling? All textbooks don’t give examples of what if the induction failed? Can somebody do 1 example showing induction fail?

  • @alamgirkhan330
    @alamgirkhan330 3 ปีที่แล้ว +3

    Professor after pre calculus i think you do algebra or partial differential equation or real analysis

  • @andreaskoutsogiannis5795
    @andreaskoutsogiannis5795 3 ปีที่แล้ว +1

    Love you!

  • @lunganispider
    @lunganispider ปีที่แล้ว

    thank you so very much ❤

  • @user-fh2rw9zh8g
    @user-fh2rw9zh8g ปีที่แล้ว

    Thanks

  • @khiannaduke5874
    @khiannaduke5874 3 ปีที่แล้ว

    Good Afternoon Professor
    Can you please assist me with these questions
    Question 1
    An education official is interested in the percentage of the adult population over 20 years, in his city, who has read at least one book during the last year. How can he investigate this question using descriptive statistics tools?
    Question 2
    A social researcher is interested in the number of children in the households of City A that receive welfare. He does not have funding for a census nor access to official city records. How can the researcher accomplish his task using descriptive statistics tools?
    Question 3
    In an organization, most of the employees earn at the lower end of the salary scale.State a chart you would use to illustrate the salary data. Describe this salary chart using the appropriate statistical terminology. If Maya, a potential employee, is seeking general information about the company salary scale, what statistical information would you give her and why?
    Question 4
    A quality engineer is curious about the thickness of the paint on the Model A cars produced by her company. Explain how she can obtain a reliable measure of the thickness of the paint, stating clearly the characteristics of the variable she should use.
    Question 5
    Devise a research question. Use this question to explain what is (a) representative sample (b) random sample (c) variable (d) measurement/data type

  • @TechnicalDoe
    @TechnicalDoe ปีที่แล้ว

    Outstanding sir 😍😍😍

  • @scar6073
    @scar6073 3 ปีที่แล้ว

    Thank you so much! ♥️

  • @inamustaf3435
    @inamustaf3435 2 ปีที่แล้ว

    Wow absolutly prof😯

  • @iamkeeper_
    @iamkeeper_ 11 หลายเดือนก่อน

    You are the best!!!! Ty

  • @kemalware4912
    @kemalware4912 ปีที่แล้ว

    KING

  • @firstdbzmaker
    @firstdbzmaker 3 ปีที่แล้ว

    Please do a course on discrete math!

  • @nervous711
    @nervous711 2 ปีที่แล้ว

    What if there's some sequence in which the pattern remains until n reaches a very large number and we aren't aware of it?

  • @rupendrakushwah
    @rupendrakushwah 3 ปีที่แล้ว

    Thnx u professor u r very helpful for me I'm from India ❤️❤️❤️❤️❤️ love from India u help me in my lyff ❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️ a great thanks u dear I pray to god that God will help u ❤️❤️❤️❤️❤️❤️

  • @The_Angry_BeEconomist
    @The_Angry_BeEconomist 3 ปีที่แล้ว

    lol @ "I like to treat my assumptions as fact" said every economist ever 3:10

  • @riwasabri6483
    @riwasabri6483 3 ปีที่แล้ว

    Hi !! Love your videos. Could you please to a Linear Algebra series? Thanks !!

  • @tanmoydey1012
    @tanmoydey1012 3 ปีที่แล้ว +2

    Not a single trigonometry function video in precalculus 73 video series... Why sir ??

    • @eobardrush2112
      @eobardrush2112 3 ปีที่แล้ว +2

      Because you will know trigonometry is a few videos away if you actually watch his videos. He already said that a few videos back

    • @tanmoydey1012
      @tanmoydey1012 3 ปีที่แล้ว

      @@eobardrush2112 thanks for replying & for the info. Brother....👍

  • @alamgirkhan330
    @alamgirkhan330 3 ปีที่แล้ว +1

    And very helpfull

  • @adhilmuhammed9402
    @adhilmuhammed9402 3 ปีที่แล้ว

    I love learning math from superman ❤️

  • @wilsonguo1580
    @wilsonguo1580 3 ปีที่แล้ว +4

    How many proofs do I need to do for arms like that? Please provide a proof lol

  • @WforWrath
    @WforWrath 3 ปีที่แล้ว

    you are a saint