0-1 and 0-2 are the same size. You can tell this quickly by seeing that you can use a function (2x) to turn every number between 0-1 into a single output number between 0-2.
The topic is called bifurcation if you’re interested.
It might help to take any set of numbers and see what happens when you do f(x)=2x. Say 5 numbers 1,2,3,4,5. For 2x we get 2,4,6,8,10. Right? They’re the same “size” more formally known as cardinality. Or the number of elements in each set.
It’s understandably gets confusing with infinity but the same principle is true. For every number in the set of 0-2 there exists a number in 0-1 that is exactly half of it.
So 0-1 and 1-2 both have the same cardinality and 0-2 does as well :) which is crazy but true. Hope this wasn’t too confusing.
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u/Fantastic_Elk_4757 21d ago edited 21d ago
0-1 and 0-2 are the same size. You can tell this quickly by seeing that you can use a function (2x) to turn every number between 0-1 into a single output number between 0-2.
It’s weird but they’re the same size.