Thank you. Miss Trowbridge, may I present Mr. Robert Rainsford. Miss Eve Trowbridge.

So let me do an example where I don't just have Rn,

But I'm not curious just about B, I want to think about ALL the points.

So if I were to write the span of a set of vectors, v1, v2, all the way to vn, that just means the set of all of the vectors, where I have c1 times v1 plus c2 times v2 all the way to cn let me scroll over all the way to cn vn.

So it's the set of let me write it this way, so I can write in the set of notations.

These are rice cakes.

I'm sure you are already familiar with.

I just defined R2 and R3, so let me define Rn.

Ready, set, let's all transform!

linear algebra is someone will write they won't just write the set of all real numbers, they'll write Rn.

It is mapping us from 2 to 8.

Let's say I have the equation y is equal to x plus 3.

It will make our denominator 0.

I could keep adding things above and below 32.

We'll shade in everything above negative 75 as well.

We get 6 is equal to x, so the domain of this function is equal to the set of all real numbers except 6.

I could also have an outline and any type of fill.

If you're interested in what it costs I'm not selling them today but this unit, with the electronics and everything, if you buy one, is around a thousand bucks.

And that's because they're easy to draw.

More formally, in supervised learning, we have a data set and this data set is called a training set.

So, embryonic stem cells are really incredible cells.

So pretty much all regular numbers that you ever dealt with before you learned what i was.

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If it's not, we have to look it up from the database, and that's how we do it.

Which means you take all of the multiples of v1, and all of the positions that they specify will create a set of points, and that is my line l.

I'm just saying that this function is generally mapping from members of this set to that set.

And, folks, the knockout is only

And you could make the horizontal axis the real axis.

In particular, it's a set of strings that can be represented by a finite state machine or a regular expression.

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So everything I've shaded in yellow is included in our solution set.

Well, the range is all of the functions, all the values that f of x can take on.

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A function really is just a relation between the members of one set and the members of the other set.

That s it. Nothing more.

So if I imagine that is my set x, and that this is my set y and y doesn't have to be smaller, that's just the way I drew it the function is just a relation.

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B a very high weight.

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Let's go over a little bit of vocabulary.

So if you ever see this, an R with an extra backbone like that, or sometimes it's written as just a really bold faced R if it's maybe typed in a book, a really bold faced R, this just means, the set of all real numbers.