[分析] 1-1 onto 的問題

[Rudin5566 (魯丁.嗚嗚溜溜)]

Is there a function from (0,1) onto [0,1] ? Prove or disprove it.

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※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 59.127.20.9
→ keroro321   :f:(0,1) -> [0,1] 1-1 and onto
→ keroro321   :是嗎?
→ keroro321   :f連續 ->沒有  , f不連續 ->有
推 zombiea     :fix irrational number, shift rational number by 2
→ zombiea     :by countability of rational number
推 CNSaya      :sin(4x)
→ CNSaya      :...沒看到1-1 囧