We said this could be any constant and this could be any constant.

It could be 1 2, it could be 10.

We can keep doing that.

I mean, we don't know what they are.

We could say, plus c, but just so that we can simplify it a

I hope that doesn't confuse you.

Let's say I have this bizarre looking function.

And you could see that even this holds.

Repeated Any Number of Times

What's the definition of the Laplace transform?

Before we said when f of x is equal to x squared that x is just any real number.

This right here is e to the minus st times f of t.

2 is just one little point in R.

Actually let's do something else just to clean it up a

So we first want to evaluate 1 to the 1st power, and anything to the first power is just that anything.

In this case 2, 3, and 5 are the prime factors of 30.

let's call them k's.

And you can just subtract them from both sides.

But once again, c is an arbitrary constant.

You get the point

And, you know, we could have some base a.

But imagine if it was, you know, an n by n by n cube.

It's pretty simple code.

To be clear, imagine the universe of all numbers and ignore the primes.

Well, and you could look at this visually

Matches an arbitrary amount of whitespace.

And this is a much faster way of evaluating the Laplace

Let's ignore c for a little bit.

This is our box.

Now.

And you could look up e other places.

You must have these parentheses.

If we want to say there's no dirt in any location, it's a little bit more complicated.

Any

When t is equal to infinity, what is x?

Well, we could put any value in for x.

We could make the ddmin even more generic by also passing the test function as a parameter.

So, non zero number.

This goes there. This matches that part.

Here's our first loop. Let's think about what we know

I think you see a pattern here.

Here we've got 5 trailing digits. Here we've got 0 of them.

So I'm going to say all real numbers.

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