this post was submitted on 23 Oct 2024
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[โ€“] [email protected] -2 points 1 week ago (3 children)

Your explanation is wrong. There is no reason to believe that "c" has no mapping.

[โ€“] [email protected] 1 points 6 days ago

because I assumed continuous mapping the number c is between a and b it means if it has to be mapped to a natural number the natural number has to be between 22 and 23 but there is no natural number between 22 and 23 , it means c is not mapped to anything

[โ€“] [email protected] 2 points 1 week ago

Give me an example of a mapping system for the numbers between 1 and 2 where if you take the average of any 2 sequentially mapped numbers, the number in-between is also mapped.

[โ€“] [email protected] 2 points 1 week ago* (last edited 1 week ago)

Yeah, OP seems to be assuming a continuous mapping. It still works if you don't, but the standard way to prove it is the more abstract "diagonal argument".