Isn't this what transfinite numbers are about? I don't remember the details, only references to 'closed infinity' and 'open infinity'. It's still an infinite number either way, i.e. it's utterly endless, but a 'closed' definition of infinity is "all numbers between x and y" where an 'open' infinite value is simply "all numbers".

Something like that, there are people who can understand and explain this infinitely better than me.