Oy vey.
If I do this quote by quote, I'll end up in an endurance race.
If I cut all the fat out and just show you where you seem confused, you'll chastise me for quoting you out of context.
And if I go nuts and ban you because I'm the King, a lot of people who normally scream ADMIN ABUSE BOO HOO will congratulate me on my rational decision making.
...
I hate you all.
So, bear with me here:
i+1 occurs after i though, even when the current i+1 is considered i.
Yes, but "the next" is always after "the current",
Right...
whether i=0, 1, 100, n, or infinity.
Right...
Infinite progression still doesn't mean you suddenly reverse direction.
And... lost you. Linguistically or mathematically we're not talking about that.
Problem numero uno is, you keep using i, when the ill-advised math analogy uses
k pretty specifically to mean "any number that is a positive integer". Not a constant. This is important, and the nomenclature you threw out that I naively ran with means I have no idea if we're talking about the same thing or not.
The idea is not that i comes after i+1, but that
k and
k+1 describe an iteration, and in the next iteration, what WAS
k+1 is now
k, and what is now
k+1 was - pause for readability -
k+1+1.
Not
k.
Which is the idea you seem to have latched onto somehow with...
Yes, there is A THING after IT. IT is not after A THING.
and
No, "one thing after another" is NOT the same thing as "one thing after the next". A thing occurring after something that is after itself is logically impossible; a thing occurring after something is not.
So what we have here is:
k+1+1: One thing after the next, or one thing after another.
k+1: The next, or another.
k: Not specified in either case. It is certainly NOT referred to as "one thing" and I don't know why you're obsessed with that idea.
I'll grant that "another" is somewhat more specific in the case that "one thing" occurs after something besides "this thing", but "the next" is linguistically accepted as meaning, specifically, "the next after the current". Next time, next customer, next door.
"Next Tuesday", of course, is an inconstant that everybody hates. Don't use that.
The word "another" does not imply a chronological order; the words "after" and "next" do.
So "one thing after the next" would be better, right? Because it specifically implies a chronological progression, where "one thing after another" could simply refer to something occurring after something else, at some point. "This is just one thing after another" starts to become something Yogi Berra would say. Yogi Berra probably did say it.
"The other" -- well, I suppose the definite article throws a wrench in the works of a visual implying an endless stream of things, but unlike "the next" it still makes logical sense in an inductive proof.
What are you defining as "the other"? It sounds more like x and y, not
k and
k+1.
"the next" implies that i follows i+1
Why do you think this?
"One after the next" (i follows i+1) rolls off the tongue but is nonsensical.
Oh that's why.
If you're conflating this with something like "Tuesday after the next", I can see where you get into the TIME PARADOX argument. But it's invalid. "One" or "one thing" is just that, a thing, not defined.
k, not i. "After the next thing after this thing, is another thing." Not "After the next thing after this thing, is this thing." Otherwise it would be "This after the next," which isn't at all impossible and describes an actual cycle, but sounds kind of dumb.
I think that when people say that phrase, what they mean is that there is "one thing" that happens "after the next", but the thing "after the next" in their context doesn't apply to the "one thing". There is an implied pile of things on their plate, which, "after the next" thing has occurred, there is "one thing" piled on top of that heap as well. In list form:
x y z b a...etc
At least that's how I've understood that phrase to mean.
Ugh fuck if I knew I'd have to have an argument about my humor analogy I'd have gone with stack (EDIT: queue) in the first place.
