It fails, and the number of subsets is 3.

Neither removal of these subsets would fail, so now we have to increase the granularity by coming up with now four subsets.

And this is what the function of all subsets returns.

But now our input only has 8 characters, and we can't split an 8 character input into 12 subsets unless these subsets would be empty.

So I see emotions as highly evolved subsets of your capability.

And this is just all the possible subsets, including the set itself.

So what the all subsets method really does is it takes a list, let's say list 1, 2, 3, and it returns all of the subsets of that list.

So you would have the empty list and you would also have the subsets containing just one element and then all the subsets containing two elements or sub lists

We split the input into initially two subsets, and if any of these subsets fails, as in here, we proceed with this very subset, otherwise, we simply go and increase the granularity, that is, we double the number of subsets and we go again to step one.

Those acronyms are all subsets of context free languages or context free grammars.

Second, if removing any of these subsets fails, proceed with this very subset.

We might have two interesting subsets that are the same size, that's possible.

This is not the right answer, because we now need to remove these subsets.

Now to get all the subsets, which is something called a power set, if you're familiar with set theory, we run it through this other function called all subsets that takes a

Because if it's not interesting, none of its subsets are going to be interesting either.

Should we now go and start again with two subsets, that is, setting n to 2 or should we go and set n to the number of subsets we had before minus 1 because there's 1 less?

Now, at this point we have gone through all the subsets and either some complement has failed.

This is a 10 character input, so each of our subsets will have between two and three characters.

So, we set n to n 1, which means that in our case we would have three subsets.

And then once we're all done with checking through all possible subsets, we just return the best test.

We're going to design together formal grammars that exactly capture HTML and JavaScript or at least interesting subsets of them.

And then an even bigger one by making the set of all the subsets of that one. And so on.

I keep saying subsets really these are lists and it's not strictly the same thing, but we can treat them

like that for now. And then all the subsets containing three elements, which is actually just the overarching list itself.

So we run through all the subsets of test and I will go through how we implemented that in a second.

So, here's how delta debugging works first, we split the input into n subsets where initially n has a value of 2.

If you prefer a more math y explanation, for us this is the same problem as given a set, print all the subsets.

At this point, n is equal to three, so we need to split the the input that is, the select tag into three subsets.

This means that, once you have one infinity, you can always make a bigger one by making the set of all subsets of that first set.

Removing any of these subsets will result in a passing test, which means that we again have to increase the granularity by doubling n in here.

Cantor also showed that, for any infinite set, forming a new set made of all the subsets of the original set represents a bigger infinity than that original set.

And by making smaller abstraction layers and smaller layers, we're going to be able to solve subsets of these problems and not have to change everything here in the middle, just one.

In the clustering problem we are given an unlabeled data set and we would like to have an algorithm automatically group the data into coherent subsets or into coherent clusters for us.

The brain has this complex task of putting together, integrating, subsets of these regions into something that's more meaningful, into what we would consider to be objects, as you see on the right.

Now we split the input into six subsets, resulting in six more attempts to remove individual parts all of them will pass and then we have to increase the granularity again, which would be 12.

If the input list had 5 entries, if you invited 5 friends to your dinner party, how many possible subsets or arrangements, ranging from no one shows up to everyone shows up, would there be?

And for every element smaller in all the possible subsets of the test list, we check if first of all the length of the subset is less than the current best size the current size of the of an interesting test list and that this element is also interesting.

And it turns out there are sometimes other versions of gradient descent that are not batch versions but instead do not look at the entire traning set but look at small subsets of the training sets at the time, and we'll talk about those versions later in this course as well.