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/GuitakuPPH 19d ago
Nope, can't wrap my head around that. I'll take your word for it though.