Extrapolation and interpolation methods

Proof by induction.

It is introspective, and I want to introspect.

And the way I'm going to prove it to you is by induction.

And we are done. That is our proof by induction.

This implies that clustering would have to be combined with extrapolation techniques.

to the year in question. This implies that clustering would have to be combined with extrapolation techniques.

The way you do a proof by induction is first, you prove the base case.

Now spoken in generalaties let's actually prove this by induction.

Then he stood before the fire and looked me over in his singular introspective fashion.

Then in our induction step, we are going to prove that if you assume that this thing is true, for sum of k.

So induction proof is almost obvious, but you can even see it based on this.

And you can put a t n here and use an inductive argument to figure out a general formula.

You see how this induction step is kinda like a domino, it cascades and we can go on and on forever so it works for all positive integers.

But if you see a couple of examples and you see a pattern there you can often extrapolate and get to a kind of broader generalization.

Learning requires some degree of extrapolation, converting randomized evaluations from hard evidence into soft evidence.

Problem? What problem? There is no problem, Grandpa.

By contrast, reckless reality testing and unnecessary risk taking are often part of bad luck.

Houston, you have a problem... Problem.

Big, big problem.

It's okay, it's okay.

So there is a catch. There is a catch.

It really is a problem.

This process is an engineering problem, a mechanical problem, a logistical problem, an operational problem.

It was a problem. A real problem.

Trouble!

Wrong? No, sir.

Matter?

A storm?

Difficulty?

Such simple extrapolations of current economic growth rates often turn out to be mistaken because of unforeseen events.

And then we're going to do the induction step, which is essentialy saying If we assume it works for some positive integer K , then we can prove it's going to work for the next positive integer, for example K 1.

And the problem of poor vision, is actually not just a health problem, it's also an educational problem, and it's an economic problem, and it's a quality of life problem.

In other words, categorize equipment problem from a people problem.

But it's a human problem. It's a scientific problem, if you will.

So if we know it is true for 1 in our base case then the second step, this induction step must be true for 2 then.

I got a problem. So it's like, OK. OK. I got a problem.

It was not only a financial problem, but also a humanitarian one.

39. Another problem is the acquisition of land.

It is not a minority or indigenous people apos s issue.

It's because it's a big problem, and it's complicated and messy.

(Laughter) So it's like, OK, I've got a problem.

I have a problem.

No problem!

We have a problem.