My picture explanation looks nicer :d

It's very understandable that people have a hard time understanding it, and it does seem counter-intuitive at first, which is why you have to try to provide proofs that are just as intuitive to understand. However when people start to deny it and claim that the math is wrong, then it's no longer so understandable, as it seems more like a knee-jerk reaction because they don't want to be bothered with understanding the concept, so denouncing it as wrong is simpler. If people don't understand it: that's completely fine. However that doesn't mean they can deny it, because it's still correct.

That said, I agree with what you have written.

Doesn't this all come down to Zeno's Paradox? We can't truly know the answer unless we can measure down to units which simply cannot be divided any further, which we haven't accomplished yet.

Another proof:

0.999...
= 0.9 + 0.09 + 0.009 + ...
= 9 * 0.1 + 9 * 0.01 + 9 * 0.001 + ...
=¹ -9 + (9 * 1 + 9 * 0.1 + 9 * 0.01 + 9 * 0.001 + ...)
=² -9 + 9 /  (1 - 0.1)
= -9 + 9 / 0.9
= -9 + 10
= 1

(1): I subtracted 9, and added 9 in in the form of 9 * 1, plus I added parentheses. Makes no difference because -9 + 9 = 0, which makes absolutely no difference in the sum.
(2): It's a geometric series, whose sum is well known. In case you didn't know, a geometric series is a series that has the form a + ar + ar^2 + ar^3 + ..., and its sum is known to be a / (1 - r), assuming|r| < 1. The sum formula is quite easy to prove and there's nothing special about it, so there shouldn't be anything controversial going on there. Here we simply have a = 9 and r = 0.1.

Anyway, the whole thing is because of the decimal notation. Nothing special about the numbers, it's just the notation that fails at this level.

Yeah, I'm not arguing the math at all.  I just wanted to add some perspective.  I have no problem with what you've been posting. 

This is not the same as Zeno's Paradox, though I suppose you could say they are somewhat related. However we have figured out Zeno's Paradox (in math terms), so it doesn't matter. When thinking of Zeno's Paradox as a mathematical conundrum, the part you said about measuring doesn't apply. You don't measure stuff in math. If you were to attempt an experiment based on Zeno's Paradox though, it would indeed come down to measurement of units and what not (until eventually you reach the planck length), but that's not what Zeno's Paradox is actually about.

If you want an explanation of how we've "solved" Zeno's Paradox, here you go:

https://www.youtube.com/watch?v=u7Z9UnWOJNY

Basically, Zeno's Paradox is more like a philosophical or logical paradox, in strict math terms, it checks out just fine.

Infinity...oh man...humans made up these concepts only because they reached a dead end while trying to hunt the truth and explain everything...even if universe explained through our mathematics makes sense to us, mathematics are only objectively correct within the rules they have been created, a reality of its own...humans created mathematics and if there are flaws in our assumptions or logic considering the universe and reality, the whole thing falls apart and cannot be used to describe anything outside the original mathematical reality...and humans can never confirm whether there are flaws while being tied to this universe and reality. Personally I think mathematics works brilliantly as an approximation.

same here.

Woah there. Physics when applied to real-world problems work brilliantly as approximations (because they are reliant on measurements, you'll never be 100% precise). Math though, is precise.

You are touching on a giant philosophical subject though: Are there inherent mathematical properties to the universe, or is mathematics just a human invention to explain the universe? Personally, I lean more to the 1st one, but this, unlike math has no right or wrong answer.

Since I'm an idiot explain to me all this because you can divide a number into ever increasingly parts until it disapears up your arse never to be seen again