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October 11, 2020 9:47 pm 30 pts
Canto Ternary Set : [1 IStage Mathematics (Poirt Set Topetogy) Denote the closed interval 10, 11 by interval into three equal part Divide the rts and remove the middle one third open interval 1, ing two disjoint open intervals Js Remaini and d, are of length J,UJ F, (say) ow again divide the above Now # Stage : Now (1) de the above two closed intervals J,, and J,, into three equal parts and middle one third open intervals of each of 1 emove the middle or Thus there remains the there relmains the following four (2) disjoint closed intervals - The length of each of the above interval= (2) Now , UJ, U J, U J,, = F, (say) Now and 0,,U n Stage e tha nth stage (2) open intervdis n, 1'n, 21--n, 2"-1 Wll be removed and there remains 2 closed ntervals L (left to right) where length of each subinterval - G) . F[0,1 F F, (1) F, (2)me F 8 9 Now U4-F, and Ul-O, Now the set OF-[0.1nUo. is called Cantor's theory sat and is denoted by (say) (ne N) k-f na 1 Remark. The set I is non-empty because the e emoved and are in tt th
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