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I am reading Anderson and Feil - A First Course in Abstract Algebra.
I am currently focused on Ch. 24: Abstract Groups ... ...
I need some help in understanding some claims in Chapter 24 by Anderson and Feil ... ...Anderson and Feil claim that ##\text{Aut}( \mathbb{R} )## is the trivial group ...
This surprises me a great deal as it seems to be saying that the number of permutations of the real number is ##1## ...! It seems to me that this should be an infinite number ... but obviously my intuition is way out ... !Can someone please explain to me why ##\text{Aut}( \mathbb{R} )## is the trivial group ...?Peter
NOTE: Anderson and Feil also claim that the groups ##\text{Aut}( \mathbb{Z} )## and ##\text{Aut}( \mathbb{Q} )## are the trivial group ... but how can this be ...?
I am currently focused on Ch. 24: Abstract Groups ... ...
I need some help in understanding some claims in Chapter 24 by Anderson and Feil ... ...Anderson and Feil claim that ##\text{Aut}( \mathbb{R} )## is the trivial group ...
This surprises me a great deal as it seems to be saying that the number of permutations of the real number is ##1## ...! It seems to me that this should be an infinite number ... but obviously my intuition is way out ... !Can someone please explain to me why ##\text{Aut}( \mathbb{R} )## is the trivial group ...?Peter
NOTE: Anderson and Feil also claim that the groups ##\text{Aut}( \mathbb{Z} )## and ##\text{Aut}( \mathbb{Q} )## are the trivial group ... but how can this be ...?