kurokotetsu said:
The sum of all problems betweem 0.9 and 1, and infinities.
I understand where you're going with this (They covered this in college, I swear!), but I must differ (on the first part) and confuse (on the infinite part). I understand how math can insert equations into the problem to bridge the gap, so to speak, but I must view these scenarios as metaphysical thought experiments. The equation exists within a bubble put aside from the normal course of things, in terms of physical space and math. It's a hypothetical reasoning of interest which, naturally, many mathematicians flock to in order to discuss. We are doing that, even though I don't consider myself an incredible mathematician. A good one, but I've known better than myself.
Now then, the line on the graph is a means to illustrate this, but you state the notion that unto approacing infinite, there being no closer number to one, it becomes one. My mind rejects, because of course there IS a difference that exists in a non-repeating value that can be written thusly: 0.00000...01. Pi is a number that can hardly fit the space of writing, but mathematicians, of course, find shortcuts to express the number in a manner understandable. The difference between 0.9 and 1 being, of course, zero-point-however-many-zeroes-it-takes-to-put-a-one-at-equal-placement-to-the-last-nine. Those two numbers are right beside each other, and yet, separated by a forever gap that exists...probably only within whatever lies beyond higgs-boson in quantum flux and foam.
Now, comes the part where I start to sound like the guy who writes XKCD stuff. The problem of 0.9 and 1, as expressed in percentage by a vote tally. There is a vote called by 100 people to make 100%, to be effectively one in all things. Arguments are made, people are convinced and cajoled and bribed into towing the line. The vote is called. One guy says no. Crap. Okay, so arguments and whatnot to try and get him in line are made, but for various reasons - same reason he can't be ousted from the percentage itself - he can't be convinced, begged, bought, etc. He is a lynchpin, an immovable object, a contant. For whatever reason, even if it's just because you said yes and he's an asshole, he says no. So, they try to work around him. Phrase the issue differently. No. Use metaphor and analogy, being philosphical even. No. Add more numbers who are willing to say yes. No. 100% not reached. More people from all over the country. No. Allies and underlings. No. World peace is declared and everyone else on the planet lives in harmony. No. Aliens from all over the cosmos come not as conquerors, but as well-wishers to this big thing going on here, trying to fill the universe with...well...intergalactic unity. The one guy still says no, so it's not 100%. It's not the definition of a unanimous vote, where everybody, every single person in a group says the same thing. It's merely a massivelt overwhelming majority. And if they exclude the one guy from the vote, that's not making it unanimous EXCEPT by changing the rules and invalidating the problem for a viable answer.
Of course, then we approach infinity, which is a mess. I feel as though it is for reasons like this that the term 'nigh-infinity' exists, just to express something that is so high that we cannot conceive of it, but we're pretty sure it's not actually infinite. Must like how it's very very VERY hard to find out what exists deeper and deeper inside the tiniest existence of what's inside the universe, it's naturally hard to conceive of a value so tiny to separate two numbers that are very extremely close, but it's in there. It must exist because 0.9 did not become 1 naturally. It needed executive meddling, and that's just cheating.