Isomorphism under differentiation

  • #1

Main Question or Discussion Point

Is 《sinx》under differentiation a valid cyclic group.
 

Answers and Replies

  • #2
Stephen Tashi
Science Advisor
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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.
 
  • #3
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Consider sin as a row, then differentiation is cyclic, but there is not any connection with groups.
 
  • #4
FactChecker
Science Advisor
Gold Member
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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.
 

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