Eight hundred streets by feet

How far do we need to gp for a bit of freedom?

Esbjorn Svensson Trio - Eight Hundred Streets By Feet

Bride Flight

It`s simply amazing how a small country like the Netherlands can generate sometimes great masterpieces; especially in cinematography, an art enterprise that usually requires a tradition and a scale difficult to achieve in small lands.

Most of the times local productions are mediocre and boring, like this Bride Flight. Even though the story is not bad and the cast is working hard, especially on the sex scenes, I could skip a full hour of the movie, come back, and not having the feeling I missed anything (the soap opera effect).

Bride Flight (Trailer)

Are you here?

No you are not

It's hard to recall the taste of summer
When everywhere around, the chill of winter
It gets so far away

Corinne Bailey Rae "Are You Here"

Odd numbers

Let's imagine we have two bags. In one bag, let's call it N-bag we put numbered balls, in the sequence 1,2,3,...; in the other bag, let's call it E-bag, we put only the even numbered balls 2,4,6,...; the procedure is as follow:

step 1: we put ball-1 in N-bag
step 2: we put ball-2 in N-bag and another ball-2 in E-bag
step 3: we put ball-3 in N-bag
step 4: we put ball-4 in N-bag and another ball-4 in E-bag
etc.

Which bag has the most balls, N-bag or E-bag? In mathematical terms, has the set of natural numbers more elements than the set of even numbers? Intuition would say so, as we fill the N-bag at twice the pace of the E-bag. There is also this fantastic demonstration I have found.

DEMONSTRATION
Let's call N the number of elements of the N-bag, and E the number of elements of the E-bag. Let's build a bag made only with odd numbers, the O-bag. To make this bag, we take out from the N-bag an exact copy of the E-bag. Now, if the N-bag and the E-bag would have the same number of elements, the O-bag would be empty. However, by construction, the O-bag is not empty, therefore the N-bag has more elements than the E-bag.

In more mathematical language, if we call N the number of elements of the Natural number set, and E the number of elements of the even number set, then O, defined as the number of elements of the odd number set is O=N-E.
If N=E than O=0.
But there is a number 3 which is odd, and therefore O cannot be 0, which means N is not equal to E.



It looks great, only it is wrong! N=E=O, but the demonstration does not fit the margin of this post.