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 Sort of a sorting problem (Posted on 2006-08-22)
Sort the set of functions f:R→R, with R being the set of real numbers. This means you have to find an order "«" that lets you compare any two pairs of unequal functions f and g; unequal means, f(x)≠g(x) for at least one x.

More precisely, these are the requirements for the order "«" you are challenged to find:

1. If f≠g, either f«g or g«f.
2. If f«g and g«h then f«h

You might be tempted to declare f«g when f(x)<g(x) for all x but that would of course fail because e.g. f(x)=x and g(x)=-x would not be comparable with respect to your order.

For a much, much easier challenge, start by finding an order for all continuous functions.

 See The Solution Submitted by JLo Rating: 4.3333 (6 votes)

 Subject Author Date Another dud vswitchs 2006-08-25 15:35:34 re: Sorting continuous functions vswitchs 2006-08-25 13:30:33 Sorting continuous functions Steve Herman 2006-08-24 23:38:18 re(4): Still in Deep Water JLo 2006-08-24 18:20:01 re(3): Still in Deep Water Steve Herman 2006-08-24 09:11:17 re(2): Still in Deep Water Richard 2006-08-24 02:24:49 re: Still in Deep Water Steve Herman 2006-08-24 02:00:19 re: Still in Deep Water, cont. Richard 2006-08-24 01:46:10 re(3): For continuous functions... Steve Herman 2006-08-24 01:45:52 Still in Deep Water Richard 2006-08-23 18:28:02 re(2): For continuous functions... Eric 2006-08-23 17:26:45 Some Thoughts Richard 2006-08-23 17:00:17 re: For continuous functions... Steve Herman 2006-08-23 09:27:43 For continuous functions... Eric 2006-08-22 13:25:47

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