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# The Sum is Greater Than It’s Parts

Written by Raymond Santos Estrella on Wednesday, 04 September 2013. Posted in 2013

In a fit of true geekiness, I was thinking about the saying “the sum is greater than it’s parts“ while taking a shower earlier. When I got back to my desk, I quickly scribbled the inequality using summations and some topos theory. I’m not too sure about my presentation but maybe I’ll come back to this and clear it up with a better presentation if it comes to me. Here’s what it looks like:

The inequality, in plain english, says that the sum of a series of numbers is greater than the sum of all those numbers. How this could possibly come about in mathematics, I have the faintest idea. I can’t think of any possible example that could prove this particular inequality. So I guess it’s one of those sayings that has no particular application to mathematics.

That’s it, end of procrastination. Still have a long day of reading ahead!

### Update

On second thought, maybe I shouldn’t use the disjoint union $\coprod \mathrm{\Omega }$ but rather $\coprod {\omega }_{i}$ instead. Maybe this is cleaner and simpler:

$\mu \left(\left[0,1\right]\right)>\sum _{x\in \left[0,1\right]}\mu \left(\left\{x\right\}\right)$

Thoughts?

### Raymond Santos Estrella

I guess I should really make a proper writeup here. Something witty or maybe a joke to add some levity. I’ll come back to this when I have time. If you have any suggested copy that I can insert here, drop me a line.

### Comments (4)

• 04 September 2013 at 13:01 |

I don't think I understood any of that.

• 04 September 2013 at 13:34 |

Why use Topos theory? Can't you come up with the summation without it?

• 04 September 2013 at 18:53 |

Nevermind lol. This is less about writing something properly and more of showing off the new MathML functionality on the site ;)

• 04 September 2013 at 20:43 |

I'm not really sure why I put that in there in the first place. It feels right and wrong at the same time.