Yes, you can do induction on the real numbers!
Audience: undergraduate
Tags: continuityreal-analysisreal-inductioncontinuous-functionsalternate-proofsintermediate-value-theoremextreme-value-theorem
Audience: Real analysis students and calculus students who can't wait to learn real analysis! Description: Ever wished you could use mathematical induction on the real numbers instead of just the natural numbers? In this video, we dive into real induction — a powerful but little-known proof technique in real analysis that can simplify some of the subject’s most important theorems. Not only is it super-interesting by itself, but it allows you to prove some classic results in real analysis in just a few lines. Created by: Nikunj Goyal <[email protected]> and David Jelinek <[email protected]> for the channel InterContinentalBallisticMath
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This is a good introduction to real induction and the proof sketches at the end are interesting. This is a natural question that arises in many introductory proof courses. However, I object to the use of AI-generated images in the video (around 12:08), which violate the AI policy — the use of the generated images to add “visual flair” is described as “Totally not OK” in the policy.
This may a bit less entertaining visually compared to other videos, but I really liked this as this was a well lecture-supplemented video.
A nice and engaging introduction, but in the future try to make it less obvious that you are reading from the screen. The topic is interesting and as a physics student I have never heard of it before, so I will definitely remember that this exists. The presentation is also clear and structured, and the animations are visually appealing. Your voice is also easy to listen to but it sometimes feels a bit like you are rushing through a written script which makes it a bit less authentic and personal.
To solidify understanding, I think what would help is at the end, show a step by step list, an algorithm of sorts, of how to apply the induction methodology. For example: 1) identify base case, 2) prove X, 3), etc.
Excellent video. The content is novel, and the explanation is clear.
wacky real induction proofs!
Personally a bit confused by the proofs, but you know, actual analysis proofs take a long time and can be really obtuse and abstract, so I think is fair, and is still really novel.