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在自然界存在着两类不同的现象。有一类现象,在一定条件下必然发生(或必然不发生)。例如,在标准大气压下,纯水加热到100℃时必然会沸腾;同性电荷必不相互吸引,等等。这类现象称为确定性现象。初等数学、微积分学等数学知识,就是研究这类现象的数学工具。另一类现象,与确定性现象有着本质的区别,例如在相同条件下抛一枚硬币,其结果可能是正面向上,也可能是反面向上,并且无论怎样控制抛掷
There are two different types of phenomena in nature. There is a class of phenomena that must occur (or necessarily not happen) under certain conditions. For example, under standard atmospheric pressure, pure water must boil when heated to 100°C; same-like charges must not attract each other, and so on. This phenomenon is called deterministic. Mathematical knowledge such as elementary mathematics and calculus is a mathematical tool for studying such phenomena. The other kind of phenomenon is essentially different from the deterministic phenomenon. For example, if you throw a coin under the same conditions, the result may be positive or negative, and no matter how you control throwing.