/jp/ - Otaku Culture

[Anonymous No.]

Suppose that we have a set of five cats. We wish to prove that they are all the same color.

Suppose that we had a proof that all sets of four cats were the same color. If that were true, we could prove that all five cats are the same color by removing a cat to leave a group of four cats.

Do this in two ways, and we have two different groups of four cats. By our supposed existing proof, since these are groups of four, all cats in them must be the same color. For example, the first, second, third and fourth cats constitute a group of four, and thus must all be the same color; and the second, third, fourth and fifth cats also constitute a group of four and thus must also all be the same color. For this to occur, all five cats in the group of five must be the same color.

But how are we to get a proof that all sets of four cats are the same color?

We apply the same logic again. By the same process, a group of four cats could be broken down into groups of three, and then a group of three cats could be broken down into groups of two, and so on. Eventually we will reach a group size of one, and it is obvious that all cats in a group of one cat must be the same color.

If you expand by induction, this shows all groups of n cats are the same colour. therefore all cats in the world are the same colour.

[Necrobrotent No.]

Fascinating

[Anonymous No.]

I like cats.

[Anonymous No.]

Unlike the multi-cat groups, the group of one cannot share a cat with any other group.

[Anonymous No.]

y dont u just look at them n see what color they r? moran

All you've proved is that each cat is the same color as itself.

[Anonymous No.]

>>7696594
groups*

[ZUN !barYV1VtIA No.]

>>an entire statue made out of der butter

[Anonymous No.]

>>7696594
This.

[Anonymous No.]

>>7696595

[Anonymous No.]

>yeah man induction totally still works if you don't have a base case and if you work backwards

Is OP just trying to see how many people on /jp/ don't understand proofs?

[Anonymous No.]

>>7696594
Mind you, you can still break them down into half-cats and quarter-cats and so on, then recombining the bits.
Sort of like mixing a bunch of soluble chemicals in a beaker of water and ending up with a homogenous solution.

[Anonymous No.]

http://www.dailymotion.com/video/x12igl_happy-happy-joy-joy_fun

Let's keep some level of intellect in this thread, shall we?

[Youmu Konpaku !MyonHUTINA No.]

>suppose we had a totally nonsensical proof
>then we would arrive at a totally nonsensical conclusion

That's cool I guess, but it makes me wonder why someone bothered thinking of this.