But it turns out that for some learning problems, what you really want is not to use, like, three or five features.

When t is equal to infinity, what is x?

So, even though we're familiar with only a few irrationals,

There's finite series, and infinite series.

You have an infinite number of possibilities here and an infinite number of possibilities here.

And I hope you understand what I'm saying, right? e to an infinity negative number approaches 0, while e to an infinitely positive number is just infinity.

How many answers are there to this?

So typically, programs are very big and accept an infinite set of inputs.

Now , Zeno might say,

You also do it for infinity, because infinity really isn't a normal number, so to speak.

And my gut sense is if you think about it, you have an infinite number of real numbers.

This would be another representation of my vector b.

So what happens as this term, right here, goes to infinity?

And so by the same intuitive argument, you could say that the limit from minus infinity to infinity of our Dirac delta function of t dt is also going to be 1.

Well you can't get much bigger than Pi, the mathematical constant.

I'm going to tell you that if I were to take the integral of this function from minus infinity to infinity, so essentially over the entire real number line, if I take the integral of this function, I'm defining it to be equal to 1.

So we're faced with this astounding conclusion

Well as we approach infinity, e to the infinity just gets bigger and bigger and bigger, right?

They're considered part of the Mandelbrot set.

We could go up into the millions of polygons.

infinity

forever

infinite

Infinity

Infinity?

One there, one there.

Well, we're going to make these rectangles really skinny and just sum up an infinite number of them.

A is an exponent right here.

And if he does this an infinite number of times, which you can do in mathematics, he ends up with an infinite number of lines, each of which has an infinite number of points in it.

Remember that the width of the confidence interval decreases with the n.

As mathematicians have since realized, it is possible to add up infinitely many finite sized terms and still get a finite answer.

Endless

Infinite

Infinite and Patch Primitives

infinite

No limit

No Limit

Any

unlimited

Never

Unlimited

As it is

since there are infinitely many of terms on the right side of the equation, and each individual term is finite, the sum should equal infinity, right?

Or we could write the solution set being from including 5 3 to infinity.

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