I was wondering what Q/Z, or the rational numbers modulo the integers.

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SUMMARY

The discussion centers on the concept of Q/Z, which represents the rational numbers modulo the integers. It is established that in Q/Z, only the fractional part of a rational number is significant, meaning that numbers like -3/4, 1/4, and 5/4 are equivalent as they share the same fractional distance from an integer. Participants confirm that rational numbers with the same signed fractional distance from an integer belong to the same coset in Q/Z.

PREREQUISITES
  • Understanding of rational numbers and their properties
  • Basic knowledge of modular arithmetic
  • Familiarity with cosets and equivalence relations
  • Concept of integer division and fractional parts
NEXT STEPS
  • Study the properties of cosets in group theory
  • Explore modular arithmetic with rational numbers
  • Learn about the structure of Q/Z and its applications
  • Investigate the relationship between Q/Z and other mathematical constructs like the unit circle
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Mathematicians, students of abstract algebra, and anyone interested in the properties of rational numbers and modular arithmetic.

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I was wondering what Q/Z, or the rational numbers modulo the integers. I am struggling to visualize what the cosets may be.

Thank you for your time.
 
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If we represent an element of Q/Z by a rational number, only the fractional part is significant. i.e. -3/4, 1/4, and 5/4 all name the same element of Q/Z.
 


Oh ok i think I get it, so rational numbers that are the same signed fractional distance from an integer are in the same coset of Q/Z?
 

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