You have a nice looking apple, And you just kept cutting it, smaller and smaller pieces.

n is any positive integer and i is zero.

I'll do a simple example here.

So the absolute value of 1 is just positive version of 1 which is just 1.

So then that equals 1.081.

And it makes sense because 0.2 , if you want to think about it, that's smaller than even one percent.

Have you ever tried to see that if you have Vaseline in front of your eyes?

Use less than or greater than for this little brackets thing to write a true sentence.

They're smaller than the shacks.

We start off with this pos variable set to 0. We loop through all the values in the list.

X2 test, well that is just a much smaller value.

We'll think a little bit more about how to remember that.

So let's just literally divide 21 into 16.

Now is this this is the function we're working with

Or, the other way to think about it is the absolute value of negative 1 is clearly less than 2.

If you took this without the absolute value signs, it is also true that 9 is less than 7.

I kept this abstract.

And the size of the room is not that big.

So this fraction, the numerator here is less than the denominator.

I don't know if that confuses you or not.

Or the absolute value of 2 is less than 3.

So 2 is clearly the smaller number here so we clearly get 2 is less than 3.

It is seen from, in this case, from outside the orbit of Saturn.

Do I take it to the left is that the decimal representation will always be smaller than the percent representation.

Lets just start here. If alpha is too small then what I'm going to do is gonna multiply the update by some small number.

I only have 2 to give away.

That only happens to some babies when they're really, really little.

Don't you have anything smaller than this?

Don't you have anything smaller than this?

Well in this case there are a lot of them.

The degree of the numerator in this part of the fraction, I guess you could call it, is going to be 1 less than that.

So before I give the example, the general idea is a negative number is any number less than zero.

We really don't want this to be n here because our inductive step is going to assume this true for everything smaller than n and not equal to n but the reality is this is actually a tiny little bit less than n.

This is smaller than that.

is less than

Less Than

less than

lesser

Any of the longer edges we're assuming we can't take negative weight edges that would cause this four to get smaller than the three.

5 is definitely larger well, at least it's equal to 5, so if I subtract maybe I'll get a 0 there.

So the lower the top of this pyramid becomes, the smaller n becomes.

What must such an algorithm look like?

The smaller the absolute value of the fraction.

In the old times it was very lively.

If we have 5 here let's just draw a circle around it because we know it's not gonna equal to 5 because we're just deciding between greater than or less than.