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## Intro to absolute value

## Video transcript

- [Instructor] In this video, we're going to introduce ourselves to the idea of absolute value, which you can view as,
how far are you from zero? So for example, let's say that we have a bunch
of people living on a street. And let's say that we say
that the school is at zero, and we could think
about other people live. So let's say I live three miles to the right of the
school, maybe that's east. So this is where I live. So that's me right over here. And that you live three miles
to the left of the school. So this is where you would
be, three miles to the left. Or maybe we could say that's
to the west of the school. Now you could say that your position is at negative three miles
relative to the school. And my position is at positive three miles relative to the school. But what we might care about is just how far are we from the school? And so there, you could say, well, we're each exactly
three miles from the school. You're three miles from the school, and I am three miles from the school. And that's what absolute value
is actually trying to get at. So for example, your
position is negative three, but if we were to take the absolute value, which you denote by these
two straight up down bars around the number, then we say, that's just going to be
your distance from zero, which is just going to be three miles. Similarly, my position is at three
miles, positive three miles. The absolute value of that is going to be, drum roll, please. It is going to be three as well. You might already see a pattern. If you're taking an absolute
value of a negative number, you get the number without the negative. And if you take the absolute
value of a positive number, it just equals itself again. But the reason why that is the case is because we're just saying, how far is that thing from zero? Let me give you another example. Let's say that we have
some type of a cruise ship, and that's the water right over there. This is the cruise ship. Let me draw it. It's this big cruise
ship, nice and big one, has water slides on it, and whatever else, whatever you would expect
from a huge cruise ship. And let say, we think about the height of where the different
floors are in the ship. And a natural place to think about is based on where the sea level is. So we call that height zero. Now there's this big waterfall
pool type thing up here. Let's just say, it's a pool
for simplicity, on the roof. And let's say that that is
at an altitude of 80 feet. So we would call that at positive 80 feet. And let's say the engine
room is right over here. And if you wanted to know its position, its height, well, it is
going to be below zero, it's below sea level, let's
say it's at negative 20 feet. So that would give you its position. One is 80 feet above the sea level, and then one is 20 feet
below the sea level. But if you just wanted
to know how far they are, well, you could take the absolute value. How far is that roof deck pool? Well, you take the absolute value of 80. You are going to get 80. How far is that engine room from zero? How far is it from sea level? Well, the absolute value of
negative 20 is going to be 20.