# euler's number

Published articles for euler's number.

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## The Inequality

DevFeed: [The Inequality](<https://devfeed.tech/articles/the-inequality-40392.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2015/11/23/the-inequality/>)

Published: 2015-11-23T22:06:27Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [math](<https://devfeed.tech/topics/math.md>), [Computer science](<https://devfeed.tech/topics/computer-science.md>), [Machine Learning & Artificial Intelligence](<https://devfeed.tech/topics/machine-learning-artificial-intelligence.md>), [Algorithms](<https://devfeed.tech/topics/algorithms.md>)

Tags: [calculus](<https://devfeed.tech/tags/calculus.md>), [cauchy-schwarz](<https://devfeed.tech/tags/cauchy-schwarz.md>), [chernoff-bound](<https://devfeed.tech/tags/chernoff-bound.md>), [computer-science](<https://devfeed.tech/tags/computer-science.md>), [euler-s-number](<https://devfeed.tech/tags/euler-s-number.md>), [inequality](<https://devfeed.tech/tags/inequality.md>), [machine-learning](<https://devfeed.tech/tags/machine-learning.md>), [math](<https://devfeed.tech/tags/math.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [taylor-series](<https://devfeed.tech/tags/taylor-series.md>)

### AI overview

This tutorial explains how the inequality 1+x ≤ e^x is used to bound the probability of bad events in machine-learning algorithm analysis and introduces its use in proving the weighted arithmetic-geometric mean inequality.

### Source excerpt

Math and computer science are full of inequalities, but there is one that shows up more often in my work than any other. Of course, I'm talking about $$\displaystyle 1+x \leq e^{x}$$ This is The Inequality. I've been told on many occasions that the entire field of machine learning reduces to The Inequality combined with the Chernoff bound (which is proved using The Inequality). Why does it show up so often in machine learning?