Acceptance of transfinite numbers

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SUMMARY

Transfinite numbers are accepted as legitimate mathematical entities, despite not being part of the real number system. They have defined operations and properties, fulfilling the criteria necessary for classification as numbers. The discussion emphasizes the importance of clarifying the definition of "genuine numbers" to understand the acceptance of transfinite numbers in mathematics.

PREREQUISITES
  • Understanding of number systems, including real and transfinite numbers.
  • Familiarity with mathematical definitions and properties of numbers.
  • Basic knowledge of set theory and its implications on number classification.
  • Concept of operations defined on mathematical entities.
NEXT STEPS
  • Research the properties and operations of transfinite numbers in set theory.
  • Explore the implications of Cantor's work on transfinite numbers.
  • Learn about the distinctions between different number systems, including real, complex, and transfinite numbers.
  • Investigate philosophical perspectives on the nature of numbers and mathematical existence.
USEFUL FOR

Mathematicians, educators, and students interested in advanced number theory and the philosophical implications of mathematical definitions.

brianhurren
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Are Transfinite numbers accepted as genuine numbers?
 
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Of course they are. They are NOT part of the real number system but they have been defined, operations defined on them, properties deduced. Everything we require of numbers.

(Perhaps you should try to make clear exactly what you mean by numbers.)
 
brianhurren said:
Are Transfinite numbers accepted as genuine numbers?

What does "genuine numbers" mean? How can a number system be not genuine?
 

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