infinity

There are infinities beyond infinities and that's what we study.

无穷数之外还有无穷个无穷数 那就是我们得到的结论

So infinity minus infinity could be zero.

所以说无穷减无穷应该是0

Noone had really thought carefully about whether infinities could come in different sizes, after all infinity is infinity.

思考过无穷数是否有大小之分 毕竟无穷数有无穷大 那可真是个惊天大发现

The number of occupied rooms would be infinity minus infinity, but it would be zero.

被占用的客房数应该是 无穷个减无穷个 变成0了

If I stayed on and all the other guests left, infinity minus infinity would be one in that case.

如果我留下来而所有的客人都离开了 无穷减无穷就变成1了

You can see that if two guests came in, infinity plus two is infinity.

如果是两个客人入住的话 无穷+2=无穷

But you see one of the problems with infinity is that it has some paradoxical properties and very basic questions about infinity that we can't answer.

关于无穷数一个问题是 它有一些自相矛盾的属性 而一些关于无穷数的基本问题我们还无法回答

Cantor's great initial discovery was that the infinity of the decimal numbers was larger than the infinity of the counting numbers.

康托的一个伟大发现就是 无穷小数集要比 无穷自然数集要大

The anger this bred almost cost me the thing that I valued above all else my memories of you, the daughter I still love infinity times infinity.

这种愤怒几乎吞噬了我 曾经最珍视的东西 我对你的记忆 我依然深爱着的女儿 无穷无尽的爱

It means there can be no matching of all the decimal numbers by the counting numbers and that tells us that the infinity of the decimal numbers is larger than the infinity of the counting numbers.

这意味着自然数集合无法 匹配于小数集合 那就是说 无穷小数集合 比无穷自然数集合要大