Name: Lec 5 | 麻省理工學院 6.00 計算機科學與程序設計導論，2008年秋季。 (Lec 5 | MIT 6.00 Introduction to Computer Science and Programming, Fall 2008)
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We should start with the confession, for those of

you looking at this on OpenCourseWare, that I'm

currently lecturing to an empty auditorium.

The fifth lecture for 600 this term, we ran into some

technical difficulties, which left us with a recording we

So, I'm-- this is a redo, and if you will hear no questions

from the audience and that's because there is no audience.

Nevertheless I will do my best to pretend.

I've been told this is a little bit like giving a speech before

the US Congress when C-SPAN is the only thing watching.

Computers are supposed to be good for crunching numbers.

And we've looked a little bit at numbers this term, but I now

want to get into looking at them in more depth than

Python has two different kinds of numbers.

So far, the only kind we've really paid any attention

And those were intended to mirror the integers, as we

all learned about starting in elementary school.

And they're good for things that you can count.

Interestingly, Python, unlike some languages, has what

By that, we mean, you can make numbers as big

We'll just take a for a variable name, and we'll set

a to be two raised to the one-thousandth power.

That, by the way, is a really big number.

And now what happens if we try and display it?

You can see why I'm doing this on the screen instead of

I'm not going to ask you whether you believe this is

the right answer, trust me, trust Python.

I would like you to notice, at the very end of

That's telling us that it's representing these-- this

The only thing to say about it is, when you're dealing with

long integers, it's a lot less efficient than when you're

And that's all it's kind of warning you, by

When you get over two billion, it's now going to deal with

long integers, so if, for example, you're trying to deal

with the US budget deficit, you will need integers of type L.

Let's look at another interesting example.

Suppose I said, b equal to two raised to the nine hundred

I can display b, and it's a different number, considerably

And now, what you think I'll get if we try a divided by b?

And remember, we're now doing integer division.

Well, you'd expect it to be two, because if you think about

the meaning of exponentiation, indeed, the difference between

raising something to the nine hundred ninety-ninth power and

to the one-thousandth power should be, in this case, two,

since that's what we're raising to a power.

Two is considerably less than two billion, and that's because

Not particularly important, but kind of worth knowing.

Well, why am I bothering you with this whole issue of how

In an ideal world, you would ignore this completely, and

just say, numbers do what numbers are supposed to do.

But as we're about to see, sometimes in Python, and in

fact in every programming language, things behave

contrary to what your intuition suggests.

And I want to spend a little time helping you understand

So let's look at a different kind of number.

And now we're going to look at what Python, and almost every

other programming language, calls type float.

And that's the way that programming languages typically

represent what we think of as real numbers.

I'm going to set the variable x to be 0.1, 1/10, and now

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Lec 5 | 麻省理工學院 6.00 計算機科學與程序設計導論，2008年秋季。 (Lec 5 | MIT 6.00 Introduction to Computer Science and Programming, Fall 2008)

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