
#1
Feb1108, 07:02 AM

P: 2,268

Can isomorophisms be really random? i.e Let f be an isomorphism and f is the operation of division if the number in the domain is bigger than 1 and multiply if it's equal to or greater then one.
Is the function f okay? It's as if 'f' can see the number before it operates on it. 



#2
Feb1108, 10:34 AM

P: 230

do you meen isomorphisms ?
if you do then: you say: Let f be an isomorphism then you try to define it? That doesn't make sence to me, and what does 'f is the operation of division' meen, what spaces does f goes from to, and division with what? When you say isomorophisms it's importent what spaces you are talking about. Fx. vector spaces you want linear bijections, metric vector spaces you wan't linear bijections that are also isometric etc. 



#3
Feb1108, 11:21 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,877

By "random" are you asking if you can just define a function any way you want and it will be an isomorphism? Certainly not! It would have to fit the definition of "isomorphism". Do you know what that is? 


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