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submitted 3 weeks ago* (last edited 3 weeks ago) by intohimo@lemmy.blahaj.zone to c/asklemmy@lemmy.ml
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[-] red@lemmy.zip 13 points 3 weeks ago

It's called countable and uncountable infinity. the idea here is that there are uncountably many numbers between 1 and 2, while there are only countably infinite natural numbers. it actually makes sense when you think about it. let's assume for a moment that the numbers between 1 and 2 are the same "size" of infinity as the natural numbers. If that were true, you'd be able to map every number between 1 and 2 to a natural number. but here's the thing, say you map some number "a" to 22 and another number "b" to 23. Now take the average of these two numbers, (a + b)/2 = c the number "c" is still between 1 and 2, but it hasn’t been mapped to any natural number. this means that there are more numbers between 1 and 2 than there are natural numbers proving that the infinity of real numbers is a different, larger kind of infinity than the infinity of the natural numbers

[-] jsomae@lemmy.ml -1 points 3 weeks ago* (last edited 4 days ago)

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

Edit: for instance, it could map to 29, or -7.

[-] red@lemmy.zip 1 points 3 weeks 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

[-] jsomae@lemmy.ml 1 points 4 days ago* (last edited 4 days 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.

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this post was submitted on 23 Oct 2024
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