Why is this "Fundamental" to arithmetic?

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This video is about the uses and importance of the "Fundamental Theorem of Arithmetic" (also known as uniqueness of prime factorisation (UPF)) which finishes with a proof of the theorem.

Further reading and motivation for the proof of UPF: https://www.dpmms.cam.ac.uk/~wtg10/FT...

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Chapters:
0:00 Introduction
1:30 Why is UPF not trivial?
7:20 Why is UPF "fundamental"?
14:19 Proof of UPF
21:40 Conclusions


(As pointed out by a comment), at 20:45 it should say "ka is less than 2p" rather than "kb is less than 2p" on the screen.

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Music:

Music by Vincent Rubinetti
Download the music on Bandcamp:
https://vincerubinetti.bandcamp.com/a...
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Candlepower by Chris Zabriskie is licensed under a Creative Commons Attribution 4.0 licence. https://creativecommons.org/licenses/...

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