互联网、手机和飞机都是人们日常使用的技术,如果没有数学和科学专业的学生发明它们,这些技术进步是不可能实现的。
The Internet, cell phones and airplanes are all technological advances that people use everyday and would not be possible without students of math and science inventing them.
没有数学,没有斜视的小字,并试图破译那些没有元音的单词。
No math, no more squinting at the fine print and trying to decipher those words with no vowels.
没有数学就没有蔬菜。
You might very well have done some very accurate math but it doesn't matter, because you did the math in the wrong place.
你可能很好地做完了一些很精确地数学运算,但是没有关系,因为你没有做错,数学运算。
So, what we are going to study now is a non-living object and we're going to pick it to be a mathematical point.
我们现在所要研究的的,是一个没有生命的物体,我们要把它看作一个数学上的点
- And in fact, mathematically if it's-- don't really have room for this.
事实上,从数学上来说-,这儿没有空间了。
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