The fact that there are no real number solutions indicates that there are no eigen vectors.

没有实数解的事实表明没有特征向量。

There's an infinite number of floating point real numbers in the world.

世界上有无数的浮点实数。

So you each of them, x1 is a member of the reals, and x2 is a member of the reals.

所以你每个人，x1 是实数的成员，x2 是实数的成员。

There was float, which is a real number with a decimal point.

有一个浮点数，是一个带小数点的实数。

You could choose any real number in the interval [0,4].

您可以选择区间[0,4]中的任何实数。

Similarly, there's a sensible notion for scaling a function by a real number.

类似地 有一个用实数缩放函数的合概念。

Now, Cantor says, start writing down a new real number.

，现在开始写下一个新的实数。

0 minus 2 is minus 2, 3, minus 1 is 2, for t is a member of the reals.

0减2等于负2,3,减1等于2,因为t是实数的一员。

And by the end of this process, you'll have a real number between zero and one.

在这个过程结束时，你会得到一个介于 0 和 1 之间的实数。

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。

So we want to think about all possible pairs of real  numbers and the XY plane comes to mind.

因此，我们想要考虑所有可能的实数对，我们会想到 XY 平面。

Our first character is Linus the Linelander, whose mind can only grasp the one-dimensional geometry of lines and the algebra of real numbers.

我们的第一个角色是莱纳斯（Linelander），他的头脑只能掌握直线的一维几何和实数的代数。

We have a complete infinite list with each integer acting like an index number, a unique identifier for each real number on the list.

我们有一个完整的无限列表，其中每个整数都充当索引号，是列表上每个实数的唯一标识符。

It shows there must be more real numbers between zero and one than there are natural numbers extending out to infinity.

它表明，零和一之间的实数必定比延伸到无穷大的自然数更多。

So an integer or a real number you'd expect to square it and it to be a positive value or perhaps zero right?

所以对于一个整数或实数，它的平方你会认为结果是一个非负数，对吗？

And now all of these points for any arbitrary-- t is a member of the real numbers, will lie on this green line.

现在，对于任何任意的 - t 是实数的成员，所有这些点都将位于这条绿线上。

It could be P2 minus P1-- because this can take on any positive or negative value-- where t is a member of the real numbers.

它可以是 P2 减去 P1 - 因为它可以取任何正值或负值 - 其中 t 是实数的成员。

Just as complex numbers are a two-dimensional extension of the real numbers, quaternions are a four-dimensional extension of complex numbers, but they're not just playful mathematical shenanigans.

正如复数是实数的二维扩展一样，四数是复数的四维扩展，但它们不仅仅是有趣的数学恶作剧。

And since we're talking about real values, it's going to be ordered list of real numbers, and a 2-tuple just says it's an ordered list of 2 numbers.

既然我们谈论的是实数值，它就会是实数的有序列表，而一个 2 组只是它是一个 2 个数字的有序列表。

For this opening quiz question, each of the  random variables can take on a value in a continuous infinite range of values, all possible  real numbers.

对于这个开放测验问题， 每个随机变量都可以取连续无限范围内的值，所有可能的实数。