It's going off to infinity plus infinity, minus infinity.

This is a situation where when we take the limit we get infinity over infinity, or negative infinity or positive infinity over positive or negative infinity.

It pops up to infinity.

Is it infinity?

0 to infinity.

Well x is, you know, infinity minus any constant is still going to be infinity, or if the limit is t approaches infinity, x is still going to be infinity here.

So when you evaluate it at infinity, when you evaluate this at infinity, you're going to get 0.

So what is the limit at infinity?

So that's this evaluated at infinity.

I mean, we could put it from minus infinity to infinity, it doesn't matter.

Isn't it just infinity?

It's not just infinity.

Doesn't this equal infinity?

And it does tend to infinity.

like square root of two and pi, the infinity of irrationals is actually greater than the infinity of fractions.

And we only care from zero to infinity, so I'll only do it from zero to infinity.

Once again, infinity is important.

I said from zero to infinity.

That's infinity, isn't it?

Surely surely it's infinity.

That's why I put that infinity in parentheses.

Because obviously you can't evaluate infinity, but you could take the limit as something approaches infinity.

But even that number is minuscule compared to another number infinity.

Actually, we don't have to do it from minus infinity.

And when I say by indeterminate form I mean that when we just take the limit as it is, we end up with something like 0 0, or infinity over infinity, or negative infinity over infinity, or maybe negative infinity over negative infinity, or positive infinity over negative infinity.

This is equal to the integral from 0 to infinity.

And we have to be careful with this infinity.

When t is equal to infinity, what is x?

So e to the minus infinity is going to go to zero much faster than this is going to go to infinity.

The integral from 0 to infinity of e to the a minus s t dt.

I wondered about the infinity and the Big Bang theory.

But if I am naughty and I do this, 1 divided by 0 is equal to infinity, you would get just as equally 2 divided by 0 is equal to infinity.

So he realized he had a set whose number of elements was larger than infinity.

We don't say something is equal to infinity, OK?

So we can't say 1 divided by 0 equals infinity.

In fact, it goes racing down to negative infinity.

And we can just use the definition of the Laplace transform, so this is equal to the area from 0 to infinity, or we could call it the integral from 0 to infinity of e to the minus that's just part of the Laplace transform definition times this thing and I'll just write it in this order times f of t times our Dirac delta function.

They represent a bigger infinity that the infinity of whole numbers.

We simply cannot just assume that 1 0 equals infinity.

Taking the integral of this thing from minus infinity to infinity, since this thing is this thing, it should be the same thing as taking the integral of this thing from minus infinity to infinity.

I've made minus 1, plus 1, infinity, and 0.

Zeno's mind bending riddles have inspired mathematicians and philosophers to better understand the nature of infinity.

So when you've evaluate what's the limit of this as t approaches infinity?

It was critical with the virtual world that it be this space of truly infinite possibility.

So we're going to evaluate this as it adds to infinity and then subtract from that evaluated at 0.