Proof by Strong Induction

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  • Опубліковано 7 лис 2024

КОМЕНТАРІ • 19

  • @hayatsguild8071
    @hayatsguild8071 2 роки тому +4

    Thank you very much. I never got that in the whole semester. Tomorrow is my final. This video will save my grade. ❤️

  • @shivpatel4499
    @shivpatel4499 4 роки тому +3

    why you took P(n-2)

  • @issacoh8675
    @issacoh8675 2 роки тому

    shouldn't it be 10 < j < k (assume the < are less than or equal to signs). Although k - 2 is true for this statement, there can be situations where k - 2 is not true since everything is true starts from k. another way to say this is, if j was equal to the value on the left, then there can be situations where that statement is false so shouldn't we make the left value the value plus the lower increment number

    • @georgefsweeney
      @georgefsweeney  2 роки тому

      No, the assumption that we would have anything between 8 and k allows us to include k-2 because our base case includes the 8, 9, and 10. So, by our base case, we actually know that our situation is true from k greater than 10 as well. Our statement is really interested in values of k greater than 10, but to be strictly true, we must state that it is true for values greater than 8.

  • @maheshm4358
    @maheshm4358 Рік тому

    How we can find the easy way to identify the starting value of the strong index..is there any formula or key that can use for finding a value...

    • @georgefsweeney
      @georgefsweeney  Рік тому

      It really depends on the numbers that are involved. In my examples, you need to make sure that the two numbers are relatively prime or there will not be a series of consecutive numbers. And in these kinds of problems, you can sometimes multiply the two numbers together and that will give a you a good sense of the final value that you need for the index. For other kinds of strong induction problems, it really depends on the question or what you are trying to prove. I am sorry I couldn't be of more help on that end.

  • @sweetlikecinnamon5951
    @sweetlikecinnamon5951 9 місяців тому

    Why do you prove the amount of postage is greater than 8, not 6? Is it because that is the first value that combines 5 and 3, whereas the values before that are independent?

    • @georgefsweeney
      @georgefsweeney  9 місяців тому

      We need to have three consecutive values that can be made using 3 and 5 cent stamps so that we can just add a 3 cent stamp in the proof to create the next value in the sequence. But we cannot create a 7 cent stamp using 3 and 5 cent stamps, so we start at 8= 5+3, 9=3*3 and 10=5*2. I hope that helps.

  • @stopthecap8810
    @stopthecap8810 2 роки тому +1

    Thanks for the video. I hope to never take this class again. Discrete math is hard

    • @georgefsweeney
      @georgefsweeney  2 роки тому

      I understand. It is, but if it were easy, computer scientist would get paid nothing and everyone would do it. You can do this!

  • @syedahnafnakiburrahman5978
    @syedahnafnakiburrahman5978 Рік тому

    Prove by induction (ordinary or strong) that any amount
    (integer) of postage greater than 27 takas can be formed with a
    combination of five and eight taka coins.

    • @syedahnafnakiburrahman5978
      @syedahnafnakiburrahman5978 Рік тому

      can you help me with this pls I'm struggling on it
      can I get the solve of this pls

    • @georgefsweeney
      @georgefsweeney  Рік тому

      I was out of town when this was sent, I am sorry I couldn't get sooner. Set up how to get 27, 28, 29, 30, and 31takas. Then the proof will be to assume you can create k-4 takas and then by adding 5 takas, you get k+1.

  • @niharikapant7231
    @niharikapant7231 2 роки тому

    Thank you sir

  • @ratandeep6694
    @ratandeep6694 2 роки тому

    this was the day gunna released WUNNA

    • @stopthecap8810
      @stopthecap8810 2 роки тому

      This the funniest and random /r/playboicarti shit I ever saw. Go study idiot