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a subset A of a topological space X is called dense (in X) if every point x in X either belongs to A or is a limit point of A
an open set is an abstract concept generalizing the idea of an open interval in the real line
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Is the set of whole numbers is dense?
No. a set of numbers is dense if you always find another number in the set between any two numbers of the set. Since there is no whole number between 4 and 5 the wholes are not dense. The set of rational numbers (fractions) is dense. for example, we can find a nubmer between 2/3 and 3/4 by averaging them and this number (17/24) is once again a rational number. You can always find tha average of two rational numbers and the result is always a rational number, so the ratonals are dense!
Why is every singleton set in a discrete metric space open?
In a metric space, a set is open if for any element of the set we can find an open ball about it that is contained in the set. Well for the singletons in the discrete space, every other element is said to have a distance away of 1. So we can make a ball about the singleton of radius 1/2 ... this ball just equals that singleton since it contains only that element. So it is contained in the set. Thus the singleton set is open.
Derived Set of a set of Rational Numbers?
The derived set of a set of rational numbers is the set of all limit points of the original set. In other words, it includes all real numbers that can be approached arbitrarily closely by elements of the set. Since the rational numbers are dense in the real numbers, the derived set of a set of rational numbers is the set of all real numbers.
What is a set of points that is endless in both direction called?
An open curve
What does a sideways u mean in math?
It is used in set theory and its meaning depends on the way that it is facing. If the open end is to the right then it indicates that the first set is a subset of the second. If the open end is to the left then it indicates that the first set is a superset of the second (the second is a subset of the first).
The densest subset of real numbers is the set of fractions?
Your question is ill-posed. I have not come across a comparison dense-denser-densest. The term "dense" is a topological property of a set: A set A is dense in a set B, if for all y in B, there is an open set O of B, such that O and A have nonempty intersection. The rational numbers are indeed dense in the set of real numbers with the standard topology. An open set containing a real number contains always a rational number. Another way of saying it is that every real number can be approximated to any precision by rational numbers. There are denser sets, if you are willing to consider more elements. Suppose you construct a set consisting of the rational numbers plus all algebraic numbers. The set of algebraic numbers is also countable, but adding them, makes it obviously easier to approximate real numbers. Can you perhaps construct a set less dense than the set of rational numbers? Suppose we take the set of rational numbers without the element 0. Is this set still dense in the real numbers? Yes, because 0 can be approximated by 1/n, n>1. In fact, you can remove finite number of rational numbers from the set of rational numbers and the resulting set will still be dense in the set of the real numbers.
Is the set of whole numbers is dense?
No. a set of numbers is dense if you always find another number in the set between any two numbers of the set. Since there is no whole number between 4 and 5 the wholes are not dense. The set of rational numbers (fractions) is dense. for example, we can find a nubmer between 2/3 and 3/4 by averaging them and this number (17/24) is once again a rational number. You can always find tha average of two rational numbers and the result is always a rational number, so the ratonals are dense!
Why dense forest is a disadvantage to giraffes?
Dense forests are not a disadvantage to giraffes. Giraffes prefer savannas, open plains and dense forests where they have the room to freely roam around.
What is an open set?
Basically its a armour set that is already open
Is the densest subset of real numbers is set of fractions?
No, the irrationals are more dense.
What is the open set in topology?
There are actually more than a definition of the open set in topology. They are:A set containing every interior point.A set containing a point along the region such that you can form the open ball.
Is the set of real numbers is an open set?
Yes.
Can golf tournament player set the hole and pin?
No, the tournament committee set the pins. In the US Open, the USGA set the pins, in The Open the R&A set the pins.
Does every open dense subset U of the unit interval have Lebesgue measure 1?
No--consider the complement of the generalized Cantor set: Let 0 < a < 1. Construct a set C_1 by removing an interval of length a/3 from [0,1], then a set C_2 by removing intervals of length a/3^2 from the two remaining intervals in C_1, and so on such that C_n is the set obtained by removing 2^n intervals of length a/3^n from C_{n-1}. Then let C, the generalized Cantor set, be defined as the intersection of all the C_n. C must be closed since it is the intersection of closed sets, thus (0,1) - C is open, and you can show that (0,1) - C is dense in [0,1], and that m[(0,1)-C] = a < 1.
Is the image of an open set under a continuous mapping need not be open?
f(x) = x^{2} is a continuous function on the set R of real numbers, and (-1, 1) is an open set in R, but f(-1, 1) = [0, 1), and [0, 1) is not an open set in R. So, f is not an open function on R.
What tpye of places does the giraffe live in?
giraffe's are living in savannas,grassland or open woodland.they enjoy roaming through both dense forest and open plains.
When are superheater safety valves set to open?
after the main safety valves are open
