My Math Forum square equals line

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 June 10th, 2009, 12:53 PM #1 Member   Joined: Jun 2009 Posts: 83 Thanks: 1 square equals line Hi, can you please prove that line segment <0;1> and <0;1>x<0;1> have the same cardinality? Thanks I have also posted some question in the wrong cathegory, maybe here it will be better but I don't know how to move it here: viewtopic.php?f=40&t=8395
June 10th, 2009, 04:20 PM   #2
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Re: square equals line

Quote:
 Originally Posted by honzik Hi, can you please prove that line segment <0;1> and <0;1>x<0;1> have the same cardinality? Thanks I have also posted some question in the wrong cathegory, maybe here it will be better but I don't know how to move it here: viewtopic.php?f=40&t=8395
One approach is to use the decimal expansion.

(I won't bother with subscripts)
1d: a0a1a2a3a4.....
2d: (a0a2a4a6....,a1a3a5...)

The above is 1-1 and all points are included both ways.

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