Understanding Set R^R: Definition and Use in Function Analysis

[karnten07]

Homework Statement

What is the set R^R? Is it used to define functions and show that the function produces real solutions?

Homework Equations

The Attempt at a Solution

 

[quasar987]

X^Y usually denotes the set of functions from Y to X.

But I've also seen R^R denote an R-fold Cartesian product of R.

 

[karnten07]

X^Y usually denotes the set of functions from Y to X.

But I've also seen R^R denote an R-fold Cartesian product of R.

Okay, in this question after it writes R^R it says "of all functions from R to R", so i think they just mean that solutions are real?

 

[quasar987]

"solutions" is not the right word, but I get what you mean.

 

[karnten07]

"solutions" is not the right word, but I get what you mean.

Oh sorry, i mean the function maps to a real number.

 

[CompuChip]

Formally, R^R is indeed the set of all R-fold tuples of real numbers. That is, an element of R^R is sort of a vector, containing in each slot a real number, and having as many slots as there are real numbers.
In everyday mathematical usage we call such an object a function from R to R.