have ≠ between them upon inifinitely many given scales, where this fact is notated as 1(0(x)≠0). And do you know the secret that the set of positive integers is a subset of R?
Even though I included the link that could explain to you what a ≤ x ≤ b means in the language that math speaks with, you ignored it. Due to your total math illiteracy, you continue to hold the expression absurd.
The language that math speaks about a ≤ x ≤ b is based on collection of 0(), end exactly because a, x or b are no more than 0(), thay can't be 1(), which exists simultaneously at AND beyond the location of any given 0().
) expression, as well.
It is not less than smaller.
You still stuck under the wrong notion that a collection of distinct 0() is 1(). This collection is just there without using enumeration, and yet it is not 1().
) expression upon infinitely many scales, which has nothing to do with any kind of enumeration.The language that math speaks about a ≤ x ≤ b is based on collection of 0(), end exactly because a, x or b are no more than 0(), thay can't be 1(), which exists simultaneously at AND beyond the location of any given 0().
This fact is notated exactly by ≠ of 1(0(a)≠0(x)≠0(b)) expression or by 1(0(x)≠0
), where 1() is exactly ≠ between distinct 0(x)≠0.), where x and y are distinct (x≠y) and order has no significance.It is strange because you don't get the notion of this notation.
No, Doron. Numbers are not zero-dimensional objects; they are not points. We use numbers to locate points, that's all. There is a correspondence between numbers and points, though, but I'm not the one who will attempt the foolish feat of explaining.
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God has taken a couple of days off, and so no one really knows what Doron means. But a guess could do as an interim: The 0() and 1() expressions are indigenous to Doronetics, coz parenthesis were invented to enclose characters -- characters such as 0 and 1. Since Doron's ideas are all of the novel kind, he puts the characters outside the parenthesis. There is a guess that says that () stands for an object and the prefix number translate the whole expression as 0() = "a zero-dimensional object" and 1() = " a one-dimensional object". The objects are presumably the point and the line.
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No, we use numbers whether thay are strict or non-strict, for example:
) that he used quite recently means that the strict relation involving x is not identical to the strict relation involving y, and that is all happening in the non-strict relation 1(). He used that expression to show that 5/2, for example, doesn't have a real result. See, Doron keeps denying the existence of the linear continuum, and one of the consequences is that there exist non negative real numbers a and b with b≠0 where a/b doesn't have a real result. He can't provide an example of such two real numbers, though. Instead, he uses the strict and the non-strict arguments to show that such numbers do exist.http://www.internationalskeptics.com/forums/showpost.php?p=6444698&postcount=12016
epix said:
The reason why √2 doesn't have an "immediate" successor is that the line that models the set of real numbers is a collection of points whose number approaches infinity and there is no segment on that line that cannot correspond to a real number. This can be proven without inventing a strange symbolism, like 0() and 1().
It is more advanced, because it discovers the fact that 1() is not a collection of 0(), where the proof by contradiction stays at the level of collection of 0().
No, it's not advanced, coz it states among other things that a straight line cannot be fully covered by points. That means there exists a line segment A_____B on that line where there are no points between A and B. But since (B - A) > 0, the line segment has length m where m>0. There are many special points, and one of them is called "the mean," or the average. In this particular case, the average of A and B is
Pmean = m/2
A_____P_____B
Any line segment must have such a point. So, your claim that there exists a line segment A__B with no points between A and B amounts to a statement that a/b where b≠0 doesn't have a solution. In other words, 6/2, for example, has indeterminable result -- the fraction does not equal 3. That, of course, doesn't apply in those happy moments when you cut salami to feed your face. LOL.
What? You don't cut salami? How come?
Wow!
), such that ≠ is 1() at AND beyond 0(x) OR 0 upon infinitely many "cutting" levels.
There are strict or non-strict solutions, for example:epix said:
"≠" is exactly the non-local property of 1() w.r.t any 0(x),0
Why do you include the number base in there?
So why did you use 1 - 0.999... instead of 1 - 0.999...9?