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mdk said
Start from the concept of variable infinity. The number of values between 0 and 1 is infinite; the number of values between 0 and 2 is infinite, but greater, right? Except it can't be greater, because there's no way to quantify an infinite number, and therefore no way to compare the two. A difference must exist, but it can't be quantified. If (endless)x2 is expressed, period, then (endless) must eventually overtake that quantity, because that's what (endless) means. In this sense, 1xinfinity = 2xinfinity, and thus 1=2 -- that's not a failure of mathematics or 'LOLNOSCIENCE' or whatever, it's simply a means of expressing that boundless reality (for instance, the space into which our universe must expand) and integers don't get along.So that opens the door for a fundamental reimagining of the number system. Now the same can be done for infinity as well. We've done the thread a few times where you prove that 0.999r=1. Conceptually there is a difference, in practicality there *must* be a difference between <1 and 1, but mathematically there is not -- and the reason is simple. Integers can't account for an infinitely small difference. But we *know* there is a difference, because that's how .999r is defined -- less than one, by an infinitely small amount. Again, this isn't a case of 'LOLNOMATH,' it's just that integers are insufficient.Okay, so if differences both infinitely great and infinitely small present challenges for absolute values, how does that impact real-world applications?Well in simplest terms, imagine numbers as slices of pizza. If I have a pizza to divide among four people in a room, I give each person two slices, and we all have the same amount of pizza, right? But do we? If we calculated the angles with surgical precision, and weighed each slice to the µg, are the slices *identical* or simply 'almost identical?' In other words, does someone get 1 slice, and someone get 0.999r slices, and someone else get 1.00...01 slices? Okay, but assume that you took possible variation out of the equation. I mean carry this out to the point where we're measuring slices of pizza with electron telescopes -- couldn't we eventually safeguard the pizza-cutting process enough that we're producing identical slices? Because the very most basic building blocks of matter and energy do not simply exist. Take electrons -- at any single point in time, a quark's existence is defined as a cloud of space in which it both exists, and does not exist. The quark is a certain size, and its position is a certain area, and the two are not equal. This is the contradiction at its most basic, most irreducible level.So what about in a complex system? Think about it. If I give you 1 Car, and I give me 1 Car, do we have the same Car? Of course not.....and that's enough psycho math typing for Spam today.

... Wh-at did you even just type?

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