If I have a bunch of numbers-- and I'll draw a number line, here.

如果我有一堆数字——我会在这里画一条数字线。

Another century later,the Library of Alexandria housed nine scrolls of her work,numbering over 10,000 lines.

又一个世纪后， 亚历山大图书馆收藏了九卷她的作品， 总行数超过 10, 000 行。

For the first objective it’ll help to think of the train as a big number line.

对于第一个目标， 将火车视为一条大数线会有所帮助。

Opposites are the same distance from zero, but just on the opposite side of the number line.

对边距零的距离相同，但位于数轴的另一侧。

I think of addition and subtraction as on a number line.

我认为加法和减法就像在数轴上一样。

We have the number line tell to help you out on this one.

我们有数轴告诉你来帮助你解决这个问题。

If I draw a number line here-- let's say I have a bunch of numbers in my population.

如果我在这里画一条数字线——假设我的人口中有一堆数字。

It's just situated in such a way that overlaps with the embedding of the number line.

它只是以这样一种方式与数轴的嵌入重叠。

When we add positive numbers, we move to the right, or in the positive direction on the number line.

当我们添加正数时，我们会向右移动，或者在数轴上向正方向移动。

Interestingly, even though we can't express irrational numbers as ratios of integers, it is possible to precisely plot some of them on the number line.

有趣的是，即便我们无法将无理数表示称为整数的比例，我们却可以将它准确表现在图形之中。

You can only have a finite number of values, while the normal distribution is defined over the entire real number line.

您只能拥有有限数量的值，而正态分布是在整个实数线上定义的。

One dimensional space is really just the number line, so transformation like this takes into de vectors and spits out numbers.

一维空间实际上就是数轴 所以像这样的变换会得到向量 然后得到数字。

On a horizontal number line, do positive integers go to the left of zero, or to the right of the zero?

在水平数轴上，正整数是在零的左边还是在零的右边？

It was just defined by projecting space onto a diagonal copy of the number line.

它是通过将空间投影到数轴的对角线副本上来定义的。

You can think about this as an extension of how we think about adding numbers on a number line.

你可以把它看作是数轴上的加法运算的扩展。

And finally, positive direction is always to the right, so if you see a number line, then a larger number will always be to the right of a smaller number.

最后，正方向总是向右，所以如果你看到一个数轴，那么一个较大的数总是在一个较小的数的右边。

For all the same reasons. The Y cordon of you hat gives us the number where j hat lands when it's projected onto the number line.

因为同样的原因 帽子上的Y线给出了j帽子投影到数轴上的位置。

So by symmetry, the number where I had lands, when it's projected onto that diagonal number line, is going to be the ex coordinate of you hat.

根据对称性 当它被投影到对角线上时 这个数就是帽子的前坐标。

Since it's easier for us to think about arrows in space rather than moving all of that space to the number line.

因为我们更容易考虑空间中的箭头而不是把所有空间移动到数轴上。

Just to be clear, even though I've embedded the number line into d space like this, the outputs of the function are numbers, not two de vectors.

明确一点 即使我像这样将数轴嵌入到d空间中 函数的输出是数字 而不是两个de向量。