this post was submitted on 23 Oct 2024
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[โ€“] red@lemmy.zip 1 points 2 weeks ago (1 children)

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€“] jsomae@lemmy.ml 1 points 20 hours ago* (last edited 20 hours ago)

Then you did not prove that there is no discontiguous mapping which maps [1, 2] to the natural numbers. You must show that no mapping exists, continugous or otherwise.