Induction Question (1 Viewer)

[BIRUNI]

That Proof was interesting man

Acmilan, How would you do it?

 

[acmilan]

That Proof was interesting man

Acmilan, How would you do it?

you cant, the flaw lies:

proof of s(k+1): k+1 consists of k people plus one person, from our assumtion k people would like to stay in this topic and from our s(1) one person would like to stay on topic (that is Pluvia) so K+1 people would like to stay on topic

This is similar to me saying something like:

S(n): n = n²

S(1) is obviously true

Assume S(k) is true for some k

Proof of S(k+1): k+1 consists of k plus one numbers. From our assumption k numbers satisfy this and so does s(1), hence k+1.

The base case (ie S(1)) is already included in the k we assume, so you cant add it as an extra

 

[BIRUNI]

I am sure his solution is correct but the way he said it may make misunderstanding. He should say in s(n): we know that pluvia would like to stay on topic and the statement is "n people would like to stay on topic"

S(1): one person would like to stay on topic which is correct.
s(k): k people would like to stay on topic
S(k+1): k+1 people would like to stay on topic.

Proof of S(k+1): K+1 consists of k people and one person. from s(k) k people would like to stay on topic and from the data of the question 1 person(pluvia) wants to stay on topic.

I think he should say that this way. but there is nothing wrong with his logic;I think the use of language made misunderstanding.

Now Vafa can you prove by induction there is only one God.

 

[Riviet]

Now Vafa can you prove by induction there is only one God.

I think a proof by contradiction would be more appropriate for a statement like that.

Proof By Induction:

S(n): n people in this thread would like to stay on topic. when n is a natural number.

S(1): 1 person in this thread would like to stay on topic and this is true because Pluvia indicated that he would like to stay on topic and he/she is 1 person. Hence the statement is true for n=1

S(k): assumme k people in this thread would like to stay on topic.

s(k+1): k+1 people in this thread would like to stay on topic.

proof of s(k+1): k+1 consists of k people plus one person, from our assumtion k people would like to stay in this topic and from our s(1) one person would like to stay on topic (that is Pluvia) so K+1 people would like to stay on topic

Hece s(n) is true for n=1, it is then true for n=2 and hence for n=3 and so on for all natural numbers.

Conclusion:
Since the statement "n people in this thread would like to stay on topic" is true for 1 person and that is pLuvia, Then statement is true for n=2, it means 2 people would like to stay on topic and hence for n=3, it means 3 people would like to stay on topic and so on for all natural numbers, it means everyone in this thread would like to stay on topic.

I thought this was amusing; even those it's not completely logical, it's still worth a laugh.