Scholar Sauce | How Mathematical Induction Can Play Tricks on You! @scholarsauce | Uploaded July 2023 | Updated October 2024, 4 hours ago.
You may have heard the phrase before that "That's a horse of a different color!" Well, I'm here to tell you that there's no such thing (well, sort of...). In this video we learn about mathematical induction and how it can be used to prove that statements that depend on a natural number are true for all natural numbers n. Induction does this by showing that a base case is true, say the case where n=1, and then proves an induction step where the fact being true for n=k implies that it is also true for n=k+1. Then the two work together where the induction step applied to the base case implies that the n=2 case works and then the induction step applied to the n=2 case implies that the n=3 is true and so on. In this video we talk about these ideas in a fun and engaging way before talking about the potential pitfalls of incorrect induction arguments that can result in incorrect conclusions. In particular, we'll talk about the incorrect proof that all horses are the same color and why induction fails to work there even though at first glance it seems to work.
If you haven't yet (and you took the time to read this), please go ahead and click that subscribe button. It helps us be able to create more content like this!
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*Music*
_End of the Rainbow_
Quincas Moreira
*Images*
_The Runners_
Published in Brockton, MA in 1900
Link: loc.gov/item/2018696402
*Movie Clips (Fair Use)*
*Obtained from yarn.co*
_The Wizard of Oz_
Metro-Goldwyn-Mayer, 1939
2 clips
_Rookie of the Year_
20th Century Fox, 1993
_The Crown_
Left Bank Pictures and Sony Pictures Television, 2016
You may have heard the phrase before that "That's a horse of a different color!" Well, I'm here to tell you that there's no such thing (well, sort of...). In this video we learn about mathematical induction and how it can be used to prove that statements that depend on a natural number are true for all natural numbers n. Induction does this by showing that a base case is true, say the case where n=1, and then proves an induction step where the fact being true for n=k implies that it is also true for n=k+1. Then the two work together where the induction step applied to the base case implies that the n=2 case works and then the induction step applied to the n=2 case implies that the n=3 is true and so on. In this video we talk about these ideas in a fun and engaging way before talking about the potential pitfalls of incorrect induction arguments that can result in incorrect conclusions. In particular, we'll talk about the incorrect proof that all horses are the same color and why induction fails to work there even though at first glance it seems to work.
If you haven't yet (and you took the time to read this), please go ahead and click that subscribe button. It helps us be able to create more content like this!
-----------
*Music*
_End of the Rainbow_
Quincas Moreira
*Images*
_The Runners_
Published in Brockton, MA in 1900
Link: loc.gov/item/2018696402
*Movie Clips (Fair Use)*
*Obtained from yarn.co*
_The Wizard of Oz_
Metro-Goldwyn-Mayer, 1939
2 clips
_Rookie of the Year_
20th Century Fox, 1993
_The Crown_
Left Bank Pictures and Sony Pictures Television, 2016
