Function Notation in Real Numbers: What Does it Mean?

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Function notation in real numbers refers to mappings from one set to another, specifically from ℝ^n to ℝ^m. When R is raised to the power of 2, it indicates the Cartesian product R x R, representing a two-dimensional space. The discussion seeks clarification on the implications of R raised to the power of n, which denotes the product of n copies of R, resulting in an n-dimensional space. This concept is fundamental in understanding higher-dimensional functions and their applications. Overall, the conversation emphasizes the importance of Cartesian products in defining multi-dimensional mappings.
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f: ℝ^n→ℝ\qquad g: ℝ^n→ℝ^m
 
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Mappings or functions from a set to another set, and the sets are cartesian products of R 1, n and m times respectively.
 
if R is raised to power 2, it means R X R and the cartesian product. what about R power n? Plz explain...
 
Last edited:
Akshay_Anti said:
if R is raised to power 2, it means R X R and the cartesian product. what about R power n? Plz explain...

The product of n copies of R, as dextercioby said.
 

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