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A cute proof that makes e natural
Po-Shen Loh is a social entrepreneur and inventor, working across the spectrum of mathematics, education, and healthcare, all around the world. He is a math professor at Carnegie Mellon University, and the national coach of the USA International Mathematical Olympiad team. He has pioneered innovations ranging from a scalable way to learn challenging math live online at comparable engagement to live-streaming entertainment (https://live.poshenloh.com), to a new way to control pandemics by leveraging self-interest.
For the full article covering many properties of, including history and comparison with existing methods of teaching: PDF from arXiv. This webpage pulls out the part of the article which uses Pre-Calculus language to explain what is so natural about, while intuitively connecting the following two important properties: Pre-Calculus usually teaches a different definition of, as the limit of the expressionwhich arises from continuously compounded interest.
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