/jeopardy/

No biters?

What is logic?

What is the basis of induction?

>>8597128
Yes, just reword it to be the exact statement missing.

>>8597134
There is at least one horse of that particular colour?
Physics would be cool.

>>8597134
HINT

In the proof this line is forgotten and that's the reason the induction is wrong:

"for n " something something..

>>8597144
HINT 2

It's in the induction step..

Some horses have different colors.

Boom.

Mmm.. seems like there are different versions floating around of this so I'll write down the one I meant:

To be proven: in any set of horses H{h_1,h_2,..h_n} all horses have the same color

Proof by induction:

1) proof for n=1:

A horse has the same color as itself, so in a set H(1) = {h_1} of one horse, all horses have the same color. Q.E.D. 1

2) proof for n+1 assuming the theorem holds for n

axiom: all horses in any set H(n) H{h_1,h_2,..h_n} have the same color
To be proven: all horses in any set H(n+1) = {h_1,h_2,..,h_n,h_n+1} have the same color

take the set H(n+1) = {h_1,h_2,..,h_n,h_n+1} and look at it's subset H(n) = {h_1,h_2,..,h_n} of size n
For H(n) we can say that all horses have the same color in this set.
Now look at the subset H(2,n+1) = {h_2,..,h_n,h_n+1} also of size n
We can also say that all horses in H(2,n+1) have the same color.
Now we know that h_1 has to same color as h_2 up to h_n.
We also know h_(n+1) has to same color as h_2 up to h_n.
Therefor h_1 has the same color as h_(n+1).
Therefor all horses in any set {h_1,h_2,..,h_n,h_n+1} have the same color Q.E.D. 2

Q.E.D.

>>8597178
HINT 4

look at this line..
>2) proof for n+1 assuming the theorem holds for n
is that only things we're assuming????

>>8596741

Can I kill you?

>>8597350
no

>>8597178
Induction step doesn't work when going from n=1 to 2.

Can you please take your freshmen "I'm such a math nerd" cancer back to xkcd? We've all seen this "paradox" so many times, it's just not funny anymore.

>>8597366
I'm not a freshman nor am I "such a nerd".

The answer was obviously "for n>2".

>>8597383
*>=