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Sort of a sorting problem (Posted on 2006-08-22) Difficulty: 5 of 5
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 fg or gf.
2. If fg and gh then fh

You might be tempted to declare fg 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)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Another dudvswitchs2006-08-25 15:35:34
re: Sorting continuous functionsvswitchs2006-08-25 13:30:33
Some ThoughtsSorting continuous functionsSteve Herman2006-08-24 23:38:18
re(4): Still in Deep WaterJLo2006-08-24 18:20:01
re(3): Still in Deep WaterSteve Herman2006-08-24 09:11:17
re(2): Still in Deep WaterRichard2006-08-24 02:24:49
re: Still in Deep WaterSteve Herman2006-08-24 02:00:19
re: Still in Deep Water, cont.Richard2006-08-24 01:46:10
re(3): For continuous functions...Steve Herman2006-08-24 01:45:52
Still in Deep WaterRichard2006-08-23 18:28:02
re(2): For continuous functions...Eric2006-08-23 17:26:45
Some ThoughtsSome ThoughtsRichard2006-08-23 17:00:17
re: For continuous functions...Steve Herman2006-08-23 09:27:43
For continuous functions...Eric2006-08-22 13:25:47
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