One person can have a disproportionately high level of influence on a widespread change but really it's not changing the world unless everyone accepts it.

Then again if you're talking about forced change...like bombing or nuking shit, one person with a nuke could do a lot of world changing.. but still no one could get one alone

Base case: n=1 No one has the power to do everything. Hence, one person cannot change the world.

Assume this is true for n=k, Now consider a set of k+1 people. Label 2 of the people A and B. Take A out of the set you have a set of k people by induction hypothesis, they cannot change the world. Now put A back in and take B out you get the same result. Hence, everyone in that k+1 set together cannot change the world.

BTW, there is a flaw in that proof, see if you can find it!

@4 Why did I never think of this when doing proofs? Just start by saying it's true for one case, then assume it's true for every case!

P(n): n people cannot change the world.

One person cannot change the world <-> P(1)

Inductive step: P(k)->P(k+1): Suppose k people cannot change the world. Suppose, by contradiction, that adding one person to this group creates a group that can change the world. However, this implies that this one person has changed the world; by joining this group, they have caused the group to change the world, and have thus changed the world. This contradicts our assumption of P(1). Thus, by contradiction, k+1 people cannot change the world, and P(k)->P(k+1) is proven.

Thus, we have P(1) and P(k)->P(k+1), so by induction, P(n) for all n>0. In other words, 1 or more people cannot change the world.

because proving the base case is all that you need to do -_- .....

ReplyDeleteOne person can have a disproportionately high level of influence on a widespread change but really it's not changing the world unless everyone accepts it.

ReplyDeleteThen again if you're talking about forced change...like bombing or nuking shit, one person with a nuke could do a lot of world changing.. but still no one could get one alone

Can someone sketch the proof please because I don't think this works.

ReplyDelete^Here I'll give you a convincing proof.

ReplyDeleteBase case: n=1

No one has the power to do everything. Hence, one person cannot change the world.

Assume this is true for n=k,

Now consider a set of k+1 people.

Label 2 of the people A and B. Take A out of the set you have a set of k people by induction hypothesis, they cannot change the world. Now put A back in and take B out you get the same result. Hence, everyone in that k+1 set together cannot change the world.

BTW, there is a flaw in that proof, see if you can find it!

@4 A&B are part of K

ReplyDeleteyou can only take A out of K not k+1 because u did not assume the k+1th person cannot change the world.

I don't think you understand how induction works OP.

ReplyDeletelol 'see if you can find it' the entire thing is garbage

ReplyDeleteMy lord.. please tell me 4 is not in math...

ReplyDelete@4 Why did I never think of this when doing proofs? Just start by saying it's true for one case, then assume it's true for every case!

ReplyDeleteP(n): n people cannot change the world.

One person cannot change the world <-> P(1)

Inductive step: P(k)->P(k+1):

Suppose k people cannot change the world. Suppose, by contradiction, that adding one person to this group creates a group that can change the world. However, this implies that this one person has changed the world; by joining this group, they have caused the group to change the world, and have thus changed the world. This contradicts our assumption of P(1). Thus, by contradiction, k+1 people cannot change the world, and P(k)->P(k+1) is proven.

Thus, we have P(1) and P(k)->P(k+1), so by induction, P(n) for all n>0. In other words, 1 or more people cannot change the world.