CAJ | 학술논문

“一尺之棰，日取其半，万世不竭”是先秦“辩者”提出的著名命题．“一尺之棰”的无限分割及其逆过程，使人们第一次认识到了“积少成多”这一在有限范围内正确的原则，应用于无限领域时产生的局限和矛盾．“辩者”所构造的“尺棰命题”无可辩驳地证明了无穷多个不为零的量，其和并非都是无穷大．这一天才的发现，是中国学者早在先秦时期就已接触到无穷级数敛散性问题的有力证据．
“일척지추，일취기반，만세불갈”시선진“변자”제출적저명명제．“일척지추”적무한분할급기역과정，사인문제일차인식도료“적소성다”저일재유한범위내정학적원칙，응용우무한영역시산생적국한화모순．“변자”소구조적“척추명제”무가변박지증명료무궁다개불위령적량，기화병비도시무궁대．저일천재적발현，시중국학자조재선진시기취이접촉도무궁급수렴산성문제적유력증거．
＂A foot-long stick, which is taken half each day, will be never exhausted eternally ＂ is the famous proposition of ＂debaters＂pre-Qin Dynasty. The infinite partition and the inverse process of＂a foot -long stick＂ make people the first time realize that the ＂ many a little makes a mickle ＂is a correct principle in a limited range, and the limitations and contradictions when it is applied to an infinite field. The ＂ foot-long stick proposition＂ of ＂debaters＂ had irrefutably proofed infinite number of non-zero volumes, whose sum is not all infinitely great. The genius discovery , was a strong evidence of convergence problem of infinite series which were touched by Chinese scholars in pre- Qin Dynasty, played an important role. in the history of mathematic thought .