# What's your favorite inequality?

**URL:** <https://boards.straightdope.com/t/whats-your-favorite-inequality/523963>\
**Category:** In My Humble Opinion\
**Created:** [January 6, 2010, 9:57pm UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963 "2010-01-06T21:57:29Z")\
**Posts on this page:** 20\
**Page:** 1

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**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\
**Post date:** [January 6, 2010, 9:57pm UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963/1 "2010-01-06T21:57:29Z")

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We’ve had at least [one thread](http://boards.straightdope.com/sdmb/showthread.php?t=397126) on people’s favorite equations, so it seems fair to do the same for inequalities.

Mine is the very simple 1 - x \< e[sup]-x[/sup], which is used all over the place in probability theory. It’s very simple to prove, as well: 1 - x is the tangent line to e[sup]-x[/sup] at x = 0. Since e[sup]-x[/sup] is a convex function, it lies above its tangent line at any point. The result follows immediately.

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**Author:** ![breezman](https://avatars.discourse-cdn.com/v4/letter/b/4491bb/32.png) [@breezman](https://boards.straightdope.com/u/breezman)\
**Post date:** [January 7, 2010, 1:54am UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963/2 "2010-01-07T01:54:54Z")

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Triangle inequality.

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**Author:** ![cmyk](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cmyk/32/3353_2.png) [@cmyk](https://boards.straightdope.com/u/cmyk)\
**Post date:** [January 7, 2010, 2:22am UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963/3 "2010-01-07T02:22:14Z")

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Racial! Oh, wait…

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**Author:** ![mnemosyne](https://avatars.discourse-cdn.com/v4/letter/m/c4cdca/32.png) [@mnemosyne](https://boards.straightdope.com/u/mnemosyne)\
**Post date:** [January 7, 2010, 2:23am UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963/4 "2010-01-07T02:23:52Z")

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Chebyshev’s Inequality.

But that’s only because I like saying “Chebyshev” (I have a thing with fun words/names to say!)

Otherwise I don’t enjoy math enough to have favourite anythings!

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**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\
**Post date:** [January 7, 2010, 3:38am UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963/5 "2010-01-07T03:38:04Z")

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Given x = y  
Assume x = 1, y=2  
Ergo 1 = 2  
You gotta love it! 😃

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**Author:** ![Nicolas\_Bourbaki](https://avatars.discourse-cdn.com/v4/letter/n/ecc23a/32.png) [@Nicolas\_Bourbaki](https://boards.straightdope.com/u/Nicolas_Bourbaki)\
**Post date:** [January 7, 2010, 6:50am UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963/6 "2010-01-07T06:50:20Z")

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^ Oh dear. ☹

As for me, I’ll be the the boring one who says Cauchy–Schwarz.

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**Author:** ![Jamaika\_a\_jamaikaiake](https://avatars.discourse-cdn.com/v4/letter/j/7993a0/32.png) [@Jamaika\_a\_jamaikaiake](https://boards.straightdope.com/u/Jamaika_a_jamaikaiake)\
**Post date:** [January 7, 2010, 7:07am UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963/7 "2010-01-07T07:07:14Z")

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> [@Nicolas\_Bourbaki](#):
>
> ^ Oh dear. ☹
> 
> As for me, I’ll be the the boring one who says Cauchy–Schwarz.

Oh, that’s not boring! I actually came in to post about the Cauchy-Riemann equations, confusing them with Cauchy-Schwartz. Whatevs.

In any case, I recall [Jensen’s inequality](http://en.wikipedia.org/wiki/Jensen%27s_inequality) being pretty neat.

ETA: Us set theorists don’t really have many good ones, other than 2^k\>k for any cardinal k (Cantor).

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**Author:** ![EvilTOJ](https://avatars.discourse-cdn.com/v4/letter/e/ee59a6/32.png) [@EvilTOJ](https://boards.straightdope.com/u/EvilTOJ)\
**Post date:** [January 7, 2010, 11:26am UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963/8 "2010-01-07T11:26:52Z")

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Women’s Suffrage.

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**Author:** ![Sailboat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sailboat/32/461_2.png) [@Sailboat](https://boards.straightdope.com/u/Sailboat)\
**Post date:** [January 7, 2010, 3:32pm UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963/9 "2010-01-07T15:32:29Z")

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The imbalance of charge that causes electrons to flow, making this post, and the nerve impulses that created it, possible.

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**Author:** ![JThunder](https://avatars.discourse-cdn.com/v4/letter/j/e95f7d/32.png) [@JThunder](https://boards.straightdope.com/u/JThunder)\
**Post date:** [January 7, 2010, 8:31pm UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963/10 "2010-01-07T20:31:11Z")

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Fermat’s Last Theorem.

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**Author:** ![tdn](https://avatars.discourse-cdn.com/v4/letter/t/94ad74/32.png) [@tdn](https://boards.straightdope.com/u/tdn)\
**Post date:** [January 7, 2010, 9:13pm UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963/11 "2010-01-07T21:13:24Z")

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> [@EvilTOJ](#):
>
> Women’s Suffrage.

We need to end it. Women have suffered enough.

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**Author:** ![Gangster\_Octopus](https://avatars.discourse-cdn.com/v4/letter/g/a8b319/32.png) [@Gangster\_Octopus](https://boards.straightdope.com/u/Gangster_Octopus)\
**Post date:** [January 7, 2010, 9:18pm UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963/12 "2010-01-07T21:18:21Z")

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The classic, the Haves versus the Have Nots.

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**Author:** ![Cunctator](https://avatars.discourse-cdn.com/v4/letter/c/43a26b/32.png) [@Cunctator](https://boards.straightdope.com/u/Cunctator)\
**Post date:** [January 7, 2010, 9:23pm UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963/13 "2010-01-07T21:23:45Z")

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The value of an annuity certain for a term equal to a person’s life expectancy at any given age always exceeds the value of a life annuity for a person of that age.

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**Author:** ![tdn](https://avatars.discourse-cdn.com/v4/letter/t/94ad74/32.png) [@tdn](https://boards.straightdope.com/u/tdn)\
**Post date:** [January 7, 2010, 9:44pm UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963/14 "2010-01-07T21:44:19Z")

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> [@Jinx](#):
>
> Given x = y  
> Assume x = 1, y=2  
> Ergo 1 = 2  
> You gotta love it! 😃

You forgot to divide by 0!

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<div class="post-metadata">

**Author:** ![breezman](https://avatars.discourse-cdn.com/v4/letter/b/4491bb/32.png) [@breezman](https://boards.straightdope.com/u/breezman)\
**Post date:** [January 7, 2010, 10:00pm UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963/15 "2010-01-07T22:00:53Z")

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> [@tdn](#):
>
> You forgot to divide by 0!

That wouldn’t change anything. 0!=1. 🙂

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**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\
**Post date:** [January 7, 2010, 10:45pm UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963/16 "2010-01-07T22:45:47Z")

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Being an algebraist, mine is that when E if a finite field extension of F, then the dimension of E over F is greater than or equal to the number of automorphims of E that fix the elements of F.

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**Author:** ![Jamaika\_a\_jamaikaiake](https://avatars.discourse-cdn.com/v4/letter/j/7993a0/32.png) [@Jamaika\_a\_jamaikaiake](https://boards.straightdope.com/u/Jamaika_a_jamaikaiake)\
**Post date:** [January 8, 2010, 6:17am UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963/17 "2010-01-08T06:17:08Z")

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> [@Cunctator](#):
>
> The value of an annuity certain for a term equal to a person’s life expectancy at any given age always exceeds the value of a life annuity for a person of that age.

HEY! Who let the actuaries in here?

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**Author:** ![Boyo\_Jim](https://avatars.discourse-cdn.com/v4/letter/b/87869e/32.png) [@Boyo\_Jim](https://boards.straightdope.com/u/Boyo_Jim)\
**Post date:** [January 8, 2010, 6:46am UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963/18 "2010-01-08T06:46:15Z")

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The vagina, no question.

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**Author:** ![ice1000](https://avatars.discourse-cdn.com/v4/letter/i/a3d4f5/32.png) [@ice1000](https://boards.straightdope.com/u/ice1000)\
**Post date:** [January 8, 2010, 6:52am UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963/19 "2010-01-08T06:52:06Z")

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iam \> u

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**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\
**Post date:** [January 8, 2010, 7:39pm UTC](https://boards.straightdope.com/t/whats-your-favorite-inequality/523963/20 "2010-01-08T19:39:17Z")

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> [@breezman](#):
>
> 0!=1

Do you mean 0 != 1, or 0! = 1? (It works either way.)

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