Haven_Stranger t1_je1sct3 wrote on March 28, 2023 at 8:03 PM

Reply to Why are there multiple species of various life forms, but humans only have one? Are there other complex single-species organisms? by CyberOGa3

How about the platypus? It's the only living species in its genus, and it's also the only living genus member in its family.

The dugong is at least as lonely. It used to share a family with the Steller's sea cow, before that was hunted into extinction.

The narwhal isn't quite so lonely. It's the only species in it's genus, but it still shares a family with the beluga (which is also the only species in its genus).

In any case, Homo sapiens isn't unique in, er, being unique. It's just a question of how much diversity develops, and then how much of it survives.

Haven_Stranger t1_j29vkgd wrote on December 30, 2022 at 6:21 PM

Reply to comment by Herkfixer in There’s just as many numbers between 0 and 1 as there is from 0 to infinity. by Resinate1

Two classes? What two classes? OP specified "numbers between 0 and 1" and "[numbers] from 0 to infinity". The class involved (entailed, even) is "numbers on the number line". In other words, reals. That's one class. That's the basis of the comparison.

Both specified ranges are uncountably infinite.

Here's an easier comparison: There are as many numbers between 0 and 1 as there are between 1 and infinity. It's an easier comparison because now both sets are strictly between their bounds, the two sets don't overlap, and the bijection formula is simpler.

If A is a real between 0 and 1, and B is the matching real greater than 1, then the mapping is:

A -> 1 / B

Also

B -> 1 / A

That's it. For every real number larger than one, there exists exactly one matching number between zero and one, and vice-versa. No exceptions, no excuses, nothing left unaccounted.

The size of the two sets are exactly the same, even though the extents of the two sets are wildly different.

Also also, that's the comparison OP meant to express. Even so, the comparison posted still holds true. It just that, instead of mapping A to the inverse of B, we map A to the inverse of one more than B.

So, no, we don't have to compare reals on one side and rationals on the other, or anything else where we'd have to specify two classes. Those comparisons can be made, of course, but they're not relevant to the post.

It takes different real numbers to make it all the way out to infinity, but it doesn't take more of them. There are exactly as many real numbers greater than 1 as there are between 0 and 1.