So how can I do something finitely many times in C?

那么我如何在C语言中做有限次的事情呢？

That you tried to cram too big of a number into finitely many bits, 32.

你试图把太大的数字塞进有限的32位。

Each of the polynomials in our space will only have finitely many terms, but the full space is going to include polynomials with arbitrarily large degrees.

空间中的每一个多项式都只有有限项 但是整个空间包含了任意大阶的多项式。

In general, since every individual polynomial has only finitely many terms, its coordinates will be some finite string of numbers with an infinite tale of zeroes.

一般来说 由于每个单独的多项式只有有限个项 它的坐标将是一个有限的数字串和一个无限的零故事。