Weekend

If you've ever wondered what the weekend looks like, he looks like this.

“I'm workin for it mother fucker!”

~ Your mom on This Weekend

Definition and Origin

The weekend is defined as a 48-hour period of continuous rain and/or severe weather.

Perhaps less familiar to the layman are the origins of its mathematical proof derivative, which lie in the equally equisite and complicated art of Ninjutsu. The Weekend Proof is commonly employed by Ninjas in battles against Pirates. Due to the alarming decrease in Pirate population as a result of global warming, Ninjas seeking to augment their pirate-hunting income have started to teach classes on the proof to the proletariat.

The Weekend Proof

The proof is sketched here, for all to enjoy and tremble before:

Lemma A12

But first, a quick refresher on lemma A12, previously left as an exercise for the reader:

f(x) = ${\begin{cases}4,&{\mbox{if }}x{\mbox{ is France}}\\2,&{\mbox{if }}x{\mbox{ is anywhere else}}\end{cases}}$

This lemma, commonly known as the "French Weekend Lemma", will be assumed for the rest of this proof.

The Set W

Now, to begin! Let us define a set W of "days", where:

W = $\left\{Sunday,Monday,Tuesday,Wednesday,Thursday,Sonofthursday,Friday,Saturday,Sabbath\right\}$

It is time to apply eons of secret ninja teachings, which cannot be revealed here. After hours of reflection and kitten petting, we eventually arrive at our definition of Z (or the days comprising "the weekend").

QED

France

If you live in France, any day that ends in "Y" is part of the weekend. The number of weekend days in France that a person will see over her lifetime, N, can be summed up as follows:

$\sum _{k=1}^{N}d=\lim _{n\to \infty }{\frac {n}{0}}$

Elsewhere

If you live anywhere else, any day before which an office worker tells you that "you have the case of the Mondays", and the day before that also. The math is a bit trickier:

$\sum _{k=1}^{N}d=\oint _{C}t^{1}7\,dt-47.12y^{2}\,dy$

The above equation is a bit over-simplified; you often need to add a quantum-derived prime-factorized Taylor constant to get an accurate answer in N-space, where N > 3.

Lucky for the discerning Ninja, by this time, the Pirates have dropped out of high school. The Ninjas will have won. Only the exceedingly rare Weekend Pirate stands a chance against this technique.