Crazy sum in mathematics

Puas yog 0.999 (rov qab) sib npaug "ib"? Tej zaum koj yuav xav tsis thoob los ntawm lo lus teb ... uas yog "yog". Kuv tau hnov ​​qhov no rau ob peb podcasts dhau los ntawm ob peb lub hlis, thiab kuv tseem pom tias nws nyuaj rau kev txais lub ntsej muag muaj nqis. Txawm li cas los, Kuv tabtom tam sim no convinced thiab ntawm no yog ob peb lus pov thawj yooj yim uas .99999 puas tseeb vaj huam sib luag 1 ...

Txoj Cai 1:

Cia x = 0.9999 ...

Tom qab ntawd 10 x = 9.9999 ...

Yog hais tias peb mam li rho x ntawm ob sab ntawm qhov kev ua zauv, ces:

10x - x = 9.9999 ... - 0.9999 ...

Yog li, 9x = 9

Faib ob tog ntawm qhov kev ua zauv los ntawm 9, thiab ...

x = 1 ... uas, thaum peb pib, peb hais = 0.9999 ...

Txoj kev 2:

1/9 = 0.11111 ...

Qhib ob sab ntawm qhov kev ua zauv los ntawm 9:

9 X 1/9 = 9 X 0.11111 ... 1 = 0.99999 ...