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Earn +20 ptsQ: Why singleton set is open in R?
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Is power set of singleton set equal to null set?
No. Let A = {a} (a singleton set) then P(A) = {a, 0} where 0 is the null (empty) set.
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.
Type of sets?
1. Null set or Empty set 2. Singleton set 3. Pair set
What set is a unit set?
That refers to a set that has exactly one element. Also known as a "singleton".
Why the set of irrational number is denoted by q'?
The set of irrational numbers is NOT denoted by Q.Q denotes the set of rational numbers. The set of irrational numbers is not denoted by any particular letter but by R - Q where R is the set of real numbers.
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