It's hard to clue Doron to spark up his vision generator funny, coz he is not fond of math of the college kind. That's why he misinterprets some descriptions, which may not be the best, but are used informally anyway, coz the listeners are familiar with the real deal. Take this "point coverage," for example. I'm positive that Doron never came across the concept of limits. Suppose that you have a line segment 6 units long and you divided the length by 3. The result is a line with 3 "sub-segments" each of them 2 units long. That's neat, but hardly enough to accommodate the needs of calculus, for example, where the x-axis is in R and needs to be divided into the smallest possible segments. To accomplish that, the domain line a is divided by n, such as n → ∞. The result is identical wherever limits are mentioned:
[lim n→ ∞] a/n = 0
Without knowing what is really going in there, a person suffering from math phobia may come to the conclusion that the domain line a has been divided into infinitely many line segments each of them having its length equal to zero and therefore a is "entirely covered by points." This is not so, otherwise it would be impossible to compute the area under any curve. But the term is used with no problems, coz the real meaning is pretty much understood by everyone hanging around math except by Doron. Even though he may accept the presence of "all points in the line," he insists on some space between them, as if his discovery was hotly contested by the views of the traditional math.
There is no way to learn to swim without getting into water, and that's exactly what Doron think is possible. He never poked the concept of infinity with his pencil, so he is not aware of certain realities that govern over the x-axis populated by points whose job is nothing else but to feed a function, and so fancy points need not apply there. Of course, there is only one set R, but Doron thinks that the angels will carry him to that set, so his fine Nike shoes wouldn't get dirty by stepping into the limits and other assorted tools of "mental exercise" used in Torture Chamber High.
Maybe he is not that good in the perpendicular reasoning, as opposed to his often-mentioned parallel reasoning. That's why he stays away from the Cartesian coordinates and all that high school math for commoners. Or maybe he doesn't want to get bothered by anything like that in his serene ascend to the Doronian metric space (formerly the ionosphere) of mathematical knowledge.
No, it can't be the smallest existing element exactly because only a point has this property, no matter what further degrees are considered.
Wrong The Man, you simply unable to get the irreducibility of a line segment into a point (the smallest existing element) as an ever smaller existence, which is a present continuous state (no before\after states are involved) of parallel reasoning, that your serial-only step-by-step reasoning simply can't comprehend.
You use a cumbersome comparison. In 1997, the approximate value of pi was computed to the precision of 51,539,600,000 digits. How was it done? Surely not by using pi=circumference/diameter. Pi is an irrational number, so you can't stick p/q into an infinite loop to watch the digits go by. Irrational numbers approach their limits through series and that means through repeated addition of some function.
Do you understand that a quantitative-only view of a line segment and a point can't distinguish between their different qualities, and only a qualitative distinction between them enables one get the quantitative property of two elements?
Furthermore, do you understand that no two points (the smallest existing elements) along a line segment are distinct from each other, without the different quality of the ever smaller element between them?
Here you demonstrate your inability to think beyond any type of difference, by getting Singularity as "One of many" concept.
Your quantitative-only view prevent the understanding of Singularity as the Unity beyond any difference, which is the source of both qualitative and quantitative differences.
Are you sure that one takes only one word from some post and also enables to understand what was written in http://www.internationalskeptics.com/forums/showpost.php?p=7067681&postcount=14925 post?
epix, 3.14159...[base 10] < pi
Enjoy your "running in circles in a closed box" game.
You are forgetting to state the means of the reduction and the domain where the above action takes place and that opens the door for contradictions. If your proposition is true, then it should be conversely true as well. And so: If no line (1-dim object) is reducible to a point (0-dim object), then a point cannot be expandable to a line. But it can.
http://en.wikipedia.org/wiki/Dimension
No, you didn't. You stepped through some examples without actually following any stated rules for construction.
This was your assertion. You did not, cannot prove it to be true. And there's no point you even trying until you actually lay out the rules you are following.
Except, you haven't shown a single bijection, yet. Not one. You claimed there were bijections for finite sets between the set and its power set. So, where are the bijections for {} and for {A}? You claimed there were bijections for infinite sets between the set and its power set. You bumbled through some arbitrary "rounds" then claimed you'd succeeded. Yet, there was no bijection to look at and no proof it was a bijection.
Irrelevant. You claimed bijections existed between the members of any set and its power set. Bijections between the whole numbers and the even whole numbers is trivial and unrelated to the problem before you.
1. I'm curious about the presence of that confusion preventer "[base 10]."