Примери коришћења Cantor set на Енглеском и њихови преводи на Српски
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An explicit formula for the Cantor set is.
Consequently, the Cantor set is totally disconnected.
These two metrics generate the same topology on the Cantor set.
The number 3/10 is also in the Cantor set and is not an endpoint.
So the Cantor set is not empty, and in fact contains an infinite number of points.
See Cantor space for more on spaces homeomorphic to the Cantor set.
This calculation shows that the Cantor set cannot contain any interval of non-zero length.
A column capital from the Ancient Egyptian site of the island of Philae carries a pattern which resembles the Cantor set.
As the above summation argument shows, the Cantor set is uncountable but has Lebesgue measure 0.
Use of ternary numbers conveniently to convey self-similar structures like a Sierpinski Triangle or a Cantor set.
In the sense of cardinality,most members of the Cantor set are not endpoints of deleted intervals.
Ternary numbers can be used to convey self-similar structures like the Sierpinski triangle or the Cantor set conveniently.
We have seen above that the Cantor set is a totally disconnected perfect compact metric space.
It can also be shown that the Haar measure is an image of any probability,making the Cantor set a universal probability space in some ways.
In Lebesgue measure theory, the Cantor set is an example of a set which is uncountable and has zero measure.
Indeed, in a sense it is the only one:every nonempty totally disconnected perfect compact metric space is homeomorphic to the Cantor set.
However this construction is not unique and so the Cantor set is not universal in the precise categorical sense.
The Cantor set contains as many points as the interval from which it is taken, yet itself contains no interval of nonzero length.
It can be formed by taking a finite Cartesian product of the Cantor set with itself, making it a Cantor space.
The Cantor set consists of the points from 0 to 1 that have a ternary expression that does not contain any instance of the digit 1.
However, the set of endpoints of the removed intervals is countable,so there must be uncountably many numbers in the Cantor set which are not interval endpoints.
The Cantor set can be seen as the compact group of binary sequences, and as such, it is endowed with a natural Haar measure.
Additionally, it turns out that the ternary representation is useful for defining the Cantor set and related point sets, because of the way the Cantor set is constructed.
For a number to be in the Cantor set, it will not to be excluded at any step, it must have a numeral consisting entirely of 0's and 2's.
Since the Cantor set is the complement of a union of open sets, it itself is a closed subset of the reals, and therefore a complete metric space.
It is perhaps most intuitive to think about the Cantor set as the set of numbers between zero and one whose ternary expansion in base three doesnt contain the digit 1.
The Cantor set is sometimes regarded as"universal" in the category of compact metric spaces, since any compact metric space is a continuous image of the Cantor set; .
So there are as many points in the Cantor set as there are in[0, 1], and the Cantor set is uncountable(see Cantor's diagonal argument).
In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties.
Since members of the Cantor set are not normal, this would imply that all members of the Cantor set are either rational or transcendental.