Acceptance of transfinite numbers

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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?