April 6th, 2018, 04:42 PM  #1 
Newbie Joined: Nov 2013 Posts: 28 Thanks: 8  Question about mapping
Many years ago when I was an undergraduate student taking a math foundation class I was asked to find a bijection between the open unit interval, (0,1) and the open unit cube. Here is what I did: I mapped the point (.a1a2a3...) to (.a1a4a7..., .a2a5a8..., .a3a6a9...). Then I mapped the point (.a1a2a3..., .b1b2b3..., .c1c2c3...) to (.a1b1c1a2b2c2...) This got me full credit and my professor was very happy with the way I did it. Fast forward to last night when I was thinking about this bijection: Well .5 is in the interval (0,1) and .5=.500.... gets mapped to (.50000..., .00000...., .000000....)=(.5,0,0). I could use .4999... for .5 but what about (.500500500...) The problem is that (.5,0,0) and (.5555...,0,0) are NOT in the unit cube (it is on it!). Can this be fixed? Any other mappings you can think of (that works!) 

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