Do we use the real numbers or do we approximate?

我们用还用近似值？

If we were dealing with higher orders of infinity, such as that of the real numbers, these structured strategies would no longer be possible as we have no way to systematically include every number.

如果我们处理更高级顺序的无穷，比如，这些结构策略便不可能的，因为我们没有办法系统地包含每字。

By the way, million is a real number.

顺便说句，百。

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

您可以选择区间[0,4]中的任何。

One of the ways to get your head around this is take it as read for a moment that a qubit, unlike a traditional classical binary bit, can represent, you know, essentially a real number or the state to some extent of a system.

理解这点的法暂时接受这样事：量子比特与传统的经典二进制位不同，它可以表示或在某种程度上表示系统的状态。

And then the way the tokenization happens, there is a special place in the neural network, which is we map this integer, like number 10,001, to a vector of real numbers.

然后，在分词过程中，神经网络中有特殊的位置，我们将这样的整， 比如10,001，映射到向量。

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

我们的第角色莱纳斯线国居民，他的思维只能理解直线的维几何和的代。

You have a mapping, T for Terence, from the real numbers to the real numbers, given by X cubed divided by two.

你有映射， T 对应特伦斯， 从到，给定为 X 立除以二。

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

你可以取的值有限的，而正态分布则定义在整线上。

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

有浮点，带小点的。

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

所以对于整或，它的平你会认为结果非负，对吗？

Ordered 2-tuples where each of the numbers, so you know you could have x1, my 1 looks like a comma, x1 and x2, where each of these are real numbers.

排序的 2 元组， 其中每字，所以你知道你可以有 x1， 我的 1 看起来像逗号， x1 和 x2，其中每都。

Then I would finally be able to explain to my mother my art with real numbers.

然后我终于可以用向妈妈解释我的艺术了。

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

在这过程结束时，你会得到介于 0 和 1 之间的。

Or more real numbers between 0 and 1?

还0和1之间的更多?

Like real numbers, we can optimize them with gradient descent, right?

像样，我们可以用梯度下降法优化它们，对吧？

To motivate the case with functions that have 2d inputs and 2d outputs, let's start off simpler, with functions that just take in a real number and spit out a real number.

为了说明具有二维输入和二维输出的函的情况，我们先从简单的开始， 即那些仅接收并输出的函。

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

没有解的事表明没有特征向量。

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

世界上有无的浮点。

So all the possible vectors that you can have, where each of its components-- and the components are these numbers right over here-- where each of its components are a real number.

所以你可以有所有可能的向量，其中它的每分量 - 分量就这里的这些字 - 它的每分量都。