It isn't! The greek letter phi (φ) can mean lots of things in mathematics, but not what you're thinking. The empty set already has a fitting name, which is "the empty set", nothing else. You can represent it unambiguously with a pair of curly brackets: {}.
If you insist, though, there does exist a symbol to represent the empty set: Ø, based off of a letter in the Norwegian alphabet. Note the forward slash instead of the vertical bar. This symbol should never be confused with phi, which might have other uses in the same context.
You probably meant to ask this: Why_is_an_empty_set_a_subset_of_every_set
Equal sets are the sets that are exactly the same, element for element. A proper subset has some, but not all, of the same elements. An improper subset is an equal set.
If set A and set B are two sets then A is a subset of B whose all members are also in set B.
There is no difference between improper subset and equal sets. If A is an improper subset of B then A = B. For this reason, the term "improper subset" is rarely used.
A "subset" means you can make it out of the pieces in the original set. No matter what set you begin with, you always have the option to choose no pieces at all--that creates the null subset.
Assume that set A is a subset of set B. If sets A and B are equal (they contain the same elements), then A is NOT a proper subset of B, otherwise, it is.
The universal subset is the empty set. It is a subset of all sets.
The empty set is a subset of all sets. No other sets have this property.
Equal sets are the sets that are exactly the same, element for element. A proper subset has some, but not all, of the same elements. An improper subset is an equal set.
Suppose A is a subset of S. Then the complement of subset A in S consists of all elements of S that are not in A. The intersection of two sets A and B consists of all elements that are in A as well as in B.
If set A and set B are two sets then A is a subset of B whose all members are also in set B.
a subset is when all elements are equivalent to eachother
There is no difference between improper subset and equal sets. If A is an improper subset of B then A = B. For this reason, the term "improper subset" is rarely used.
If all elements of set A are also elements of set B, then set A is a subset of set B.
-28 belongs to: Integers, which is a subset of rationals, which is a subset of reals, which is a subset of complex numbers.
A "subset" means you can make it out of the pieces in the original set. No matter what set you begin with, you always have the option to choose no pieces at all--that creates the null subset.
Assume that set A is a subset of set B. If sets A and B are equal (they contain the same elements), then A is NOT a proper subset of B, otherwise, it is.
A proper subset is a subset that includes some BUT NOT ALL of the elements of the original set. If the subset is finite, its order must be smaller than that of the original set but that need not be the case if the two sets are infinite. For example, even integers are a proper subset of all integers but they both contain an infinite umber of elements.