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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

The Sum is Greater Than It’s Parts

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:

{ Ω | ω 1 , ω 2 , . . . , ω n } ;   Ω > 1 n ω

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 Ω but rather ω i instead. Maybe this is cleaner and simpler:

μ ( [ 0 , 1 ] ) > x [ 0 , 1 ] μ ( { x } )

Thoughts?

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About the Author

Raymond

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)

  • techim

    techim

    04 September 2013 at 13:01 |

    I don't think I understood any of that.

    reply

  • Saint Elsewhere

    Saint Elsewhere

    04 September 2013 at 13:34 |

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

    reply

  • Raymond

    Raymond

    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 ;)

    reply

  • Raymond

    Raymond

    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.

    reply

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