無窮小是以零為極限的變量,對於這種變量引用普遍的極限定義可得如下的深入的定義:若對於任何指定的正數ε,變量y在其變化過程中達到這樣一個時刻,從該時刻起y的絕對值恒保持小於ε,則變量y稱為無窮小,如n依次取所有的自然數1,2,3,…时,變量為無窮小,因為當n>100時y<0.1,當n>10000時y<0.01,一般當n>1/ε~2时y<ε。若變量y的極限為有盡數a,则極限式limy=a相當於關係式lim(y-a)=0,即相當於差(y-a)為無窮小,因此我們也可以反過來:把無窮小的定義—特殊場合 The infinitesimal is a variable whose limit is zero. For the definition of a universal limit for such a variable, an in-depth definition can be obtained as follows: If for any given positive number ε, the variable y reaches such a moment during its change, from that moment The absolute value of y is always kept less than ε, then the variable y is called infinitesimal. If n takes all natural numbers 1,2,3,... in order, the variable is infinitesimal, because when n>100, y<0.1 when n> When 10000 is y<0.01, generally y<ε when n>1/ε~2. If the limit of the variable y is an exhaustion number a, then the limit formula limy=a is equivalent to the relation lim(ya)=0, which means that the difference (ya) is infinitesimal, so we can also reverse it: the definition of infinitesimal—special occasion