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thesmokingman@programming.dev ⁨6⁩ ⁨months⁩ ago

This is incorrect. There is not a one-to-one and onto mapping from the natural numbers to the real numbers ergo the sets have a different size. We have defined words to describe this. We can put uncountably many copies of the natural numbers inside of the real numbers so there are arguably infinitely more reals than naturals.

Granted you have to accept the axiom of choice for any of this.

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weker01@feddit.de ⁨6⁩ ⁨months⁩ ago
I know. I’ve studied this extensively. I am specialized in formal logic and by extension set theory. I’ve worked with and help write actual research papers in this field where this is basic knowledge.

I’ve never claimed their to be a bijection between the reals and the natural numbers. Please point out what statement I made that is wrong. I would very much like to know.

Also no you do not have to accept choice for this to be true. ZF is perfectly acceptable to study various infinite sets with differing cardinality.

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- thesmokingman@programming.dev ⁨6⁩ ⁨months⁩ ago
  
  That does not make one set more infinite than the other. You cannot be more unending than to literally have no end.
  
  Your use of language is incorrect. But, since you’re clearly the only published expert with any experience in this topic on the internet, it’s really not worth pointing out that we fall on two sides of the standard axiom of choice debate since you already knew that. Have fun!
  
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  - weker01@feddit.de ⁨6⁩ ⁨months⁩ ago
    My use of language could very well be incorrect. I am not a native English speaker anyways. That’s no reason to be so condescending.
    
    I was just merely stating my credentials to have a basis of discussion but you do not seem to be interested in that.
    
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