Isomorphism under differentiation

[tomgotthefunk]

Is 《sinx》under differentiation a valid cyclic group.

 

[Stephen Tashi]

A group must have a binary operation involving it's elements. What are the elements of the group you are asking about? What is the binary operation?

Perhaps you are thinking that differentiation operates on a set of real valued functions. That is true, but differentiation itself is not a real valued function. (Differentiation is a function from functions to other functions.) So differentiation of a function is not a binary operation involving two real valued functions.

 

[mac_alleb]

Consider sin as a row, then differentiation is cyclic, but there is not any connection with groups.

 

[FactChecker]

You could consider differentiation operations on the set (sinx, cosx, -sinx, -cosx) where the + operation is consecutive differentiation. With a little work, I am sure you could define a cyclic group.