/sci/ - Science & Math

[Anonymous No.6051030]

Mother fucking proofs.

I can't write them. I know how a proof should work, but I can't write it in the syntax of math.

For example. The homework problem that has been boning me for the past 4+ hours.

You have a deck of cards, arranged (white heart A through K, black clover A - K, black spade A - K, white diamond A - K). You can shuffle the deck in two ways, an inner perfect shuffle and an outer perfect shuffle. For both, you start by splitting the deck in half, taking the top half in your right hand and the bottom in your left. You overlay the cards one by one from each half. An inner shuffle results in the first card in your left hand on top, the opposite for the outer shuffle.

Prove that it is impossible to reach a state where the top half of the deck are all black cards using a state machine and invariant.

I have no idea how the fuck to define a state machine so I can create some invariant to prove this. But I know that the number of white and black cards in both the top and bottom half have to stay constant. How the fuck do I express this?

[Talimar No.6051062]

It's a fucking dumb assignment.

A machine is basically a repetitive function. In this case, you are dealing with a closed system, the 52 cards.

The wording of the question doesn't state that the cards have to stay constant. It states that you have to prove somehow that producing 2 cycles of n-length are going to produce a specific arrangement of your n values. It further requests that you fuck up your math such that you insist that resolving an infinite regress proves that somehow 52 cards are incapable of actually being a mathematical model.

So, in this case, you get an n-quantity which gets divided into two n subsets; for which you mix things up.

In this case it's just a complete fuckup. Part of the problem is it gives you the option to choose whether to do an inner or an outer shuffle, which allows you to undo specific n-cycles, if you know what you are doing. (one to the left, one to the right and oh... hey, you have your top card again.)

Normally they argue that the 26 division n-cycle is never divisible by the n-4 cycle derived from suit set of your cards and makes whatever shuffling system appear as if it is infinite.

They basically argue... A(2b) = 52, but b can be called 4d that is divided by 26 (while ignoring the "A" half of the equation) and voila, you can't solve this.

They request a machine that doesn't work.