Equivalence relations problem #2 (alg)

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Homework Help Overview

The discussion revolves around an equivalence relation defined on the Cartesian product of real numbers, specifically focusing on the relationship between pairs of numbers based on the sum of their squares. Participants are tasked with finding a bijection from the equivalence classes to a set of non-negative real numbers.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the geometric interpretation of the equivalence classes and consider the implications of the relationship defined by the sum of squares. There are hints provided regarding the nature of the equivalence classes and the concept of radius.

Discussion Status

Some participants have offered hints to guide the original poster in understanding the problem better, particularly emphasizing the geometric perspective of the equivalence classes. There appears to be a mix of attempts to clarify the problem and share insights without reaching a definitive conclusion.

Contextual Notes

The original poster expresses difficulty in finding a solution similar to a previous problem, indicating a potential constraint in their understanding or approach. The hints suggest a focus on the properties of the equivalence relation and the nature of the set B.

Pearce_09
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R = the real numbers

A = R x R; (x,y) \equiv (x_1,y_1) means that
x^2 + y^2 = x_1^2 + y_1^2; B= {x is in R | x>= 0 }

Find a well defined bijection sigma : A_\equiv -> B

like the last problem, I just can't seem to find the right way to solve this??
 
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hint 1 x^2+y^2 is a positive real number.

hint 2 What is an equivalence class under this relation, think geometrically.

hint 3 radius.
 
Pearce_09 said:
R = the real numbers

A = R x R; (x,y) \equiv (x_1,y_1) means that
x^2 + y^2 = x_1^2 + y_1^2; B= {x is in R | x>= 0 }

Find a well defined bijection sigma : A_\equiv -> B

like the last problem, I just can't seem to find the right way to solve this??

did you get it?
 
ya i did thanks fourier
 

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