I need help with the following proof:

http://i27.tinypic.com/dr9hzb.jpg

Thanks

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- Jun 24th 2008, 04:58 PMhelpculesautomorphism problem
I need help with the following proof:

http://i27.tinypic.com/dr9hzb.jpg

Thanks - Jun 24th 2008, 06:45 PMNonCommAlg
suppose obviously: thus

hence for all thus: i.e.

next we show that is (strictly) increasing: let be two real numbers and then for

some thus: so: i.e. is

(strictly) increasing.

now let and choose such that call this since is

increasing, by but thus:

call this now and give us: since is arbitrary,

we must have - Jun 24th 2008, 08:38 PMThePerfectHacker
Here is another way. If we can show is continous then let be any real number and be a sequence of rationals converging to . Then by continuity . Let us show that is continous WLOG at . Let and choose . Then if we can find a rational so that and then by using the strict property as

**NonCommAlg**shown.

A more interesting question is to find .