So let's say that we wanted to compare the absolute value of 2 to the absolute value of 3.

I know your gut reaction is the natural log of y, which is correct, but there's actually a slightly broader function than that, whose derivative is actually 1 over y, and that's the natural log of the absolute value of y.

Now, you could integrate both sides of this, and you'll get the natural log of the absolute value of x is equal to the natural log of the absolute value of mu, et cetera, et cetera.

If we want to maximize the product, we can play a number of interesting tricks.

But the easy way to calculate absolute value signs, if you don't care too much about the concept is whether it's negative or positive, the absolute value of it is always going to be positive.

So in general absolute value will always be a positive quantity.

But if you had some negative numbers here, you would actually say the absolute value of numerator is lesser than the absolute value of the denominator, for a proper fraction

Because here, that obviously works for positive values, because the absolute value of x will be equal to x.

absolute

Minimal Value is a hard limit

So both of these things evaluate to 8.

But anyway, that's the left hand side, and then that equals Well, this one's easy.

If it's a positive number already, it just equals itself, when you take the absolute value.

6 Absolute Value

I'll do it in orange, the absolute value of negative 3, we just figured out, that is positive 3.

Now, this should cause you some pause, because when you take the absolute value of anything, what do you know you're going to get?

Shift to the right you get minus 1 times 2 plus 2 times 1 to zero.

So we are stilil going to have a negative number

It's saying that it has to be a negative number.

In the magenta situation, the thing in the absolute value sign was positive 2, because this was a situation where we assumed that the thing in the absolute value sign was a positive 2.

So if the absolute value of something is equal to 0, what can that something be?

But if you think about it in kind of just very simple terms, if it's a negative number, it becomes a positive version of it.

Absolute value of 10. or the absolute value of x, when x 10.

2 is 2 to the right of 0. So this is just going to evaluate to 2.

Let's do a couple more examples.

So that first value, on this number line, so all of these are absolute values.

You're going to get a non negative number.

Yeah, it's very textural.

These two numbers are exactly 2 and 1 2 away from 0, because both of their absolute values is 2 and 1 2.

This evaluates to 9. 7 is exactly 7 to the left of 0.

2 times 8 is 16, minus 5 gives 11.

2 times negative 3 is negative 6, minus 5 gives negative 11.

So you take negative 2 here.

So you'd say that the absolute value of negative 3 is equal to positive 3.

1 Absolute Value Smallest

6 Absolute Value Last

Let's do a couple more of these.

So this is going to be equal to the ( abs( 15) abs( 46) abs( 29)) and the reason why we are writing this. this might look fancy but this is really just the length of this purple arrow.

So let's think about these numbers.

So, let's just think about absolute value of x, when x 5.

That's 2.

He's an absolute idiot.

So it's just 2.

We don't even have to look at the number line, is just going to be the positive version of 12, is just going to be equal to 12. and this is saying that 12 is 12 away from 0.

Another kind of statement is the return statement.