Uploaded February 2026 | Updated September 2026, 2 weeks ago
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You might think, from your own experience, that things like whole numbers and fractions are very common. We almost can't help but think about irrational numbers such as pi and e as special numbers which are the exceptions among the number line. But in fact, almost ALL real numbers are irrational. A special few happen to grab a lot of attention, but they are not special because they're irrational. In this video we'll demonstrate the measure of the rationals is zero to establish the overwhelming preponderance of irrationals on the number line. #mathmemes #realanalysis
Outro Song: youtube.com/shorts/qp8YRBNMKds
(Longer Version: youtube.com/watch?v=Pw9aWBlCxPc )
More Math Chats: youtube.com/playlist?list=PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO
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Abstract Algebra: amzn.to/3IjoZaO
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Calculus: amzn.to/3PieD1M
Proofs and Set Theory: amzn.to/367VBXP (available for free online)
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SOURCES
Irrational Numbers by Ivan Niven
austinrochford.com/posts/2013-12-31-almost-no-rationals.html
researchgate.net/figure/Application-of-the-custom-python-based-algorithm-for-fitting-the-mono-exponential-model_fig3_391013478
0:00 Intro
2:40 The Fractions, Right?
4:28 Measuring the Integers
9:41 Measuring the Rationals
16:03 Avoiding Basel
18:02 Finishing Q
20:17 Further Discussion
21:41 Conclusion
7:01 Strongman Problem
π Check out my math fashion brand! mathshion.com
β€οΈ Join the channel to get exclusive and early videos, original music, math lectures, and more!
youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join
You might think, from your own experience, that things like whole numbers and fractions are very common. We almost can't help but think about irrational numbers such as pi and e as special numbers which are the exceptions among the number line. But in fact, almost ALL real numbers are irrational. A special few happen to grab a lot of attention, but they are not special because they're irrational. In this video we'll demonstrate the measure of the rationals is zero to establish the overwhelming preponderance of irrationals on the number line. #mathmemes #realanalysis
Outro Song: youtube.com/shorts/qp8YRBNMKds
(Longer Version: youtube.com/watch?v=Pw9aWBlCxPc )
More Math Chats: youtube.com/playlist?list=PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO
Business Inquiries: wrathofmathlessons@gmail.com
Textbooks I Like!
Graph Theory: amzn.to/3JHQtZj
Real Analysis: amzn.to/3CMdgjI
Abstract Algebra: amzn.to/3IjoZaO
Linear Algebra: amzn.to/43xAWEz
Calculus: amzn.to/3PieD1M
Proofs and Set Theory: amzn.to/367VBXP (available for free online)
Statistics: amzn.to/4d5HbUQ
Discrete Math: amzn.to/3qfhoUn
Number Theory: amzn.to/3JqpOQd
Follow Wrath of Math on...
β Instagram: instagram.com/wrathofmathedu
β TikTok: tiktok.com/@wrathofmathedu
β X: https://x.com/wrathofmathedu
SOURCES
Irrational Numbers by Ivan Niven
austinrochford.com/posts/2013-12-31-almost-no-rationals.html
researchgate.net/figure/Application-of-the-custom-python-based-algorithm-for-fitting-the-mono-exponential-model_fig3_391013478
0:00 Intro
2:40 The Fractions, Right?
4:28 Measuring the Integers
9:41 Measuring the Rationals
16:03 Avoiding Basel
18:02 Finishing Q
20:17 Further Discussion
21:41 Conclusion
7:01 Strongman Problem
