Acceptance of transfinite numbers

AI Thread Summary
Transfinite numbers are accepted as genuine numbers despite not being part of the real number system. They have been rigorously defined, with operations and properties established, fulfilling the criteria necessary for a number system. The discussion raises questions about the definition of "genuine numbers" and the implications of a number system being considered non-genuine. Clarifying what constitutes a number is essential for understanding this topic. Ultimately, transfinite numbers hold a legitimate place in mathematical discourse.
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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