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Re: Rational numbers

Hello, vdimas, you wrote: V> E-e-e... Well then for any number presented in a binary type for a basis mn-va it is possible to take items 2 e-n i, where n i - numbers of nonzero discharges of a mantissa (since seniors) and e= for floating representation or shift of a point for fixed. Then to add it mn-in derivative members under the formula (a+b+1)/2 for all pairs of items, at which |a-b | <1. To lead such addition in a cycle until in mn-ve there will be new members. It? Instead of, it is simple a finding such minimum mn-va to which posess initial number. But not accessory clearing up to minimum mn-vu, received from 0-lja.

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Re: Rational numbers

Hello, samius, you wrote: V>> As on a condition we can add and subtract these numbers to receive from them new. S> and even to subtract? Under that link it has insufficiently been told. Found the primary source, there it is written: The  interval starts when first fuse is lit, ends when last fuse goes out. I.e. it is impossible to subtract.

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Re: Rational numbers

Hello, vdimas, you wrote: V> From a condition. Growing to the right infinite otherwise turns out mn-in, i.e. speech about its minimality cannot be. The minimum set is not obliged to be restricted. Let to itself grows to the right, how many to it takes in head. The main thing that it did not have a smaller subset which too would satisfy to a statement of the problem.

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Re: Rational numbers

Hello, Kodt, you wrote: 2.xxxxxxx - since 2.0, there are all numbers Absolutely all? Or it is possible to take only numbers of finite length?

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Re: Rational numbers

Hello, Eugene Sh, you wrote: V>> From a condition. Growing to the right infinite otherwise turns out mn-in, i.e. speech about its minimality cannot be. ES> the minimum set is not obliged to be restricted. Let to itself grows to the right, how many to it takes in head. The main thing that it did not have a smaller subset which too would satisfy to a statement of the problem. I am afraid, in this case both mn-va coincide that minimum that the full. Likely meant to eliminate any totals such fusible numbers from mn-va? But here, seemingly, their any total can be deduced as sequence of "mandatory" applications of the initial formula (p+q+1)/2.

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Re: Rational numbers

Hello, Kodt, you wrote: But here we, actually, encounter a philosophical question what to consider as minimum set. It is clear that all sets, satisfying to a condition "with zero and shorted on merge" - . Simply enough to take any function - f (x) = 0@x or f (x) = x@x (where - merge operation, x@y = (x+y+1)/2) and  a countable amount of times. And it is possible to specify still about ""? For example, a generated elementary row (for a case y=0) 1-2-n is infinite, converges in a limit to 1. Or specific binary representation of number from a floating comma in the computer meant? But if we write function F (M) = M U {x@y | x, y <- M}> and we find its fixed points S fix = F (S fix) = F * (S seed) that it appears that in between it is possible to install the partial order - that whose subset is. And it is obvious that if S seed1 <= S seed2 S fix1 <= S fix2 the Absolute minimum in it, topological, sense is an empty set, but we do not set off it. The smallest seed S seed0 = {0} - on a statement of the problem. As wrote already nearby, seemingly, that any total fusible numbers as "the necessary mandatory minimum" expresses through "mandatory" application of the formula (x+y+1)/2, calculating. That is, seemingly, that join generally all (arbitrary) mn-in, satisfying to a condition, will coincide with minimum or to be its subset.

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Re: Rational numbers

Hello, vdimas, you wrote: V> And it is possible to specify still about ""? Enumerable set

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Re: Rational numbers

Hello, Eugene Sh, you wrote: V>> And it is possible to specify still about ""? ES> Enumerable set Well then required mn-in not  since it on-definition has capacity N 2, where N-capacity mn-va natural numbers.

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Re: Rational numbers

Hello, Kodt, you wrote: From here - paradoxes, for example, that the set of even natural numbers is equivalent to set of all natural numbers. Though "at home level" the set even is "less" than set of the natural. Well, I still remember it.) ) Koef at capacity is not considered, levels/logarithms are considered. For example, capacity mn-va pairwise combinations of all natural numbers will be more capacities mn-va natural numbers, expresses as N 2, where N-capacity mn-va natural numbers.> Therefore  pushed us on thin ice. 1. All suitable sets . Minimum required mn-in directly on a condition has capacity N 2. The Same capacity has mn-in rational numbers, i.e. representable in the form of simple fractions a/N b. Therefore also it wanted to specify, why ? Here it is pure for finishing to the point of irrationality: let merge operation looks so: x@y = x+y+15. Natural numbers, multiple 15 - approach. Natural numbers, multiple 3 or 5 - again approach. Natural numbers, multiple 15 or 17 - too approach, though whence undertook 17? Yes from a ceiling. All natural numbers - approach. What from this good we select from quality of "minimum"? There in these rows generated by the initial recurrence formula, merge "well works" only to value <2, i.e. when the same number  as different methods. Therefore, there  only mn-in numbers <2.

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Re: Rational numbers

Hello, Kodt, you wrote: V>> As wrote already nearby, seemingly, that any total fusible numbers as "the necessary mandatory minimum" expresses through "mandatory" application of the formula (x+y+1)/2, calculating. That is, seemingly, that join generally all (arbitrary) mn-in, satisfying to a condition, will coincide with minimum or to be its subset. How it - "join of all" will be a subset minimum?! I will try to explain. Is certain f-ija which postulates presence of certain elements in mn-ve since she says that if p and q - elements mn-va and distance / them <1 x=F (p, q) - too the element of it mn-va. It is Still given that 0 is an element of it mn-va, we accept x 0=0. Total, substituting x 0 in F, we receive: x 0:1 = F (x 0, x 0). Further: x 0:2 = F (x 0, x 0:1). x 0:3 = F (x 0, x 0:2). x 1:2 = F (x 0:1, x 0:1). x 1:3 = F (x 0:1, x 0:2). Etc. I.e. It is necessary to apply mutually F to all available and received on each step x i and x j, the distance / with which is less 1. Received mn-in I nearby named "a mandatory minimum", i.e. it and is required minimum mn-in. We argue further. We present that it is possible to take the arbitrary number r, "violently" to include it in mn-in and as mutually under the formula  still elements such mn-va. And so, if r is not the number received under the initial recurrence formula we   in what "minimum mandatory", APPRX. Simply I stated that any number, representable in the form of the total of elements x i from minimum mn-va, too is included in the magic image into it mn-in. For example: x 0:1+x 0:1=1/2+1/2=1. And the limit of some x 0:n, n-> oo too is equal 1. Still: x 0:1+x 0:2=1/2+3/4=5/4. The limit of some x 1:n, n-> oo too is equal 5/4. Etc. Further. There are still such observations: For any number of a type 2-x 0:n is mandatory there will be a row from this the most minimum mn-va, converging to this number. For example: 2 - 1/2 = 3/2 - there is such row. 2 - 3/4 = 5/4 - there is such row. 2 - 7/8 = 9/8 - there is such row. 2 - x 0:n, n-> oo = x 0:n, n-> oo = 1 2 - 0 = x 3:n, n-> oo = 2 And it is for some reason true for any number r> = 2. ., any number r> = 2, at first,  in the form of the total of elements x from minimum mn-va 1/2 <= x <= 3/2, in the second, too is included into this minimum mn-in at its recurrence calculation. Total, for numbers from a range 1/2. 1 it is enough to learn on an accessory to a row: 1/2 3/4, 7/8..., 1-2-nCHto it is elementary, if a rational number to present in the form of natural fraction. And here for numbers from a range 1. 2 it is "enough" to learn on an accessory to one of rows: 1. 1/2+3/2-1/2 1/2+3/2-3/4, 1/2+3/2-7/8... 1/2+5/4-1/2 1/2+5/4-3/4, 1/2+5/4-7/8... 1/2+9/8-1/2 1/2+9/8-3/4, 1/2+9/8-7/8...... 2. 3/4+3/2-1/2 3/4+3/2-3/4, 3/4+3/2-7/8... 3/4+5/4-1/2 3/4+5/4-3/4, 3/4+5/4-7/8...... 3. 7/8+3/2-1/2 7/8+3/2-3/4, 7/8+3/2-7/8... n.... Meanwhile there is an observation that in diagonals of everyone n- matrixes contain identical numbers, i.e. it is possible to replace each of them with its any column or a line. Total, the group of matrixes is degenerated in one matrix the accessory to which should be found... ==== it is interesting, and the HARDWARE has a decision?))

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Re: Rational numbers

Hello, vdimas, you wrote: V> Hello, samius, you wrote: V>>> On a condition on the link initially a row was under construction under other formula: S>> There is under the link no row V> Badly read, means. V> pay attention to how received 45 seconds. Turned. Two laces. A row did not note. V>>> as on a condition we can add and subtract these numbers to receive from them new. S>> and even to subtract? V> yes. Light two different chains " events", and measure time / their termination. S>> I.e.-1/2 your way too fusible. V> Only if "interval of time" can be negative.)) it follows from your thesis about possibility of subtraction for obtaining of the new. V>>> V>>> Formally, a rational number x is fusible if and only if x=a*2-b, with an and b natural numbers. S>> And at what natural an and b quits fusible-1/2, 5/8? V> 5/8 => a=5, b=3 and 1/4 at a=1 and b=2 at you fusible? So that with uniqueness p and q?

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Re: Rational numbers

Hello, vdimas, you wrote: V> Hello, samius, you wrote: S>> And even to subtract? V> under that link it has insufficiently been told. V> found the primary source, there it is written: V> V> The  interval starts when first fuse is lit, ends when last fuse goes out. V> I.e. it is impossible to subtract. Means, and statement Formally, a rational number x is fusible if and only if x=a*2-b, with an and b natural numbers. False

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Re: Rational numbers

Hello, kfmn, you wrote: K> Hello, kov_serg, you wrote: _>> . any numbers representable in the form of the total on twain levels belong S K> In a condition was about minimality S. And time so it is exact not any. What is the minimality? On capacity? Set on any infinite since if p and q belong S and p+q too belongs. For all p and q it is more or equal 1. As implication will be fulfilled in this case, for |p-q | <1 === false

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Re: Rational numbers

Hello, sr_dev, you wrote: _> That such a minimality? A minimality of set S means that it is a subset of each set,  to the specified conditions. Or, in other words, is intersection of all sets of rational numbers,  to the specified conditions.

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Re: Rational numbers

Hello, nikov, you wrote: N> Hello, sr_dev, you wrote: _>> That such a minimality? N> a minimality of set S means that it is a subset of each set,  to the specified conditions. N> or, in other words, is intersection of all sets of rational numbers,  to the specified conditions. I was mistaken about that that set on any infinite. The least on capacity set S it {0, 1} implication for it is fulfilled, for |0+1 | <1 === false Less than two elements already it is impossible. Can the task more approximately to practice as that to formulate?

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Re: Rational numbers

Hello, sr_dev, you wrote: _> Hello, nikov, you wrote: N>> Hello, sr_dev, you wrote: _>>> That such a minimality? N>> a minimality of set S means that it is a subset of each set,  to the specified conditions. N>> or, in other words, is intersection of all sets of rational numbers,  to the specified conditions. _> I was mistaken about that that set on any infinite. _> the least on capacity set S it {0, 1} _> implication for it is fulfilled, for |0+1 | <1 === false _> Less than two elements already it is impossible. The incorrect inference. Let S it {0, 1}. Then 0 and 0 belongs S. Then |0-0 | == 0 <1. Means 1/2 belongs S. And so on.