yelinna (yelinna) wrote in traveling_pics,
yelinna
yelinna
traveling_pics

  • Music:

This week’s assignment from the League: Top 1



This is a little nerdy joke I wanted to make since some time ago. Enjoy!

First, let me introduce to you all, the amazing Wau number (I watched the video and I was amazed!):



After taking a course on Measure Theory the last months, I found another cool property of the Wau number. I won't get into the gory math details, don't get scared, this will be short and simple, let's begin:

We will define the following:

Omega is a space, any space: numbers, sets, animals, squares, Higgs bosons... anything you want.
F is a set called "sigma-algebra", it allow us to define properties on Omega and work with it. F has special characteristics: it includes a set that belongs to Omega and the complement of A. F includes Omega itself and the empty set. If F includes any other set, it includes its complement and the unions and intersections of any other set that belongs to F (also includes the complements of those unions and intersections).
Next we define a probability. It is just a number between 0 and 1 that we assign to any set in F.

These three together make a Measure Space (if P is any number it is called Measure Space. If P is between 0 and 1, it is a Probability Space. So any Probability Space is also a Measure Space):


Now I will introduce to you all the Lebesgue Integral. It is just a sum of the probabilities (or measures) of the sets inside F with other special properties, but we don't need to get into details here :)

Then, the whole family looks like this:

"dP" means that the integral is tied to our probability. A is any set in our sigma-algebra F.

This integral is the same as the following:

The "1A" means "The Indicator Function of set A". This is simply that if we tak any element in F, if it belongs to A, the indicator function gives 1, otherwise it gives 0.The Lebegue integral on set A is the same as the Lebesgue integral of the indicator function of A on the whole Omega space.

And this is equal to:

The probability of set A. The number between 0 and 1 we assigned to the set A.

If we tahe the Lebesgue Integral on the whole Omega space...


You can google to find out the real value of the Wau number :D you also will know why this is a "Top 1" :D :D

Other League Members Posts:
Grey loves Board Games
Trash Culture loves old Videos
I love Movie Monsters too!
Adam loves Ghostbusters
I love that Alf clip plushie!!
Mason loves cereal
I love figurine Top Tens :D
DVD collection!
I love short stories too, Lovecraft rocks!
Top Ten Marvel Movies



<<-- Join The League!! Just a single post is needed :D
Subscribe

  • Año Nuevo 2021 / New Year 2021

    01-01-2021: Picnic en el parque (San Isidro) Picnic at the park (San Isidro) 03-01-2021 Paso entre el Rajuntay y el Uco con Bruno, Eduardo y…

  • Diciembre 2020 / December 2020

    3-12-2020 CAKE!!! 13-12-2020: Sisiscaya en Bicicleta (Provincias de Lima y Huarochirí) Sisiscaya by bike (Lima and Huarochirí…

  • Nieve Navideña / Xmas snow

    Es verano en el hemisferio sur, lo que significa lluvias y tormentas en las alturas de los Andes. It is summer in the south hemisphere, that means…

  • Post a new comment

    Error

    default userpic

    Your reply will be screened

    Your IP address will be recorded 

    When you submit the form an invisible reCAPTCHA check will be performed.
    You must follow the Privacy Policy and Google Terms of use.
  • 0 comments