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Why empty set is open on the basis of def?
The empty set is open because the statement: "if x in A, some neighborhood of x is a subset of A" is true! If A is empty, the hypothesis: "if x in A" is false and so the statement is vacuously true.
What is empty set in math?
An empty set is this { } It's just a set with nothing in it.
How come an empty sets become an empty sets?
An empty set becomes an empty set by virtue of its definition which states that it is a set that contains no elements. In other words, it contains nothing, it is empty!
Is a null set a subset of every set and Why?
Yes - because, if something is an object of the null set, then it is also an element of the other set. Since nothing is an element of the empty set, the above statement is trivially true.
Why is the empty set called a set?
Because its still a set, although its empty or nothing in that set {} {0} * * * * * The second example above is NOT of an empty set: it is the set that contains the number zero.
