Sets A and B are equivalent if A is a subset of B and if B is a subset of A. A is a subset of B if every element of A is in B. Since 0 is in 01234 but not in 12345, 01234 isn't a subset of 12345, and therefore the sets are not equivalent.
a subset is when all elements are equivalent to eachother
Irrational Numbers which are a subset of Real Numbers which are a subset of Complex Numbers ...
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.
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.
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.
-28 belongs to: Integers, which is a subset of rationals, which is a subset of reals, which is a subset of complex numbers.
Equivalent sets are sets that have the same cardinality. For finite sets it means that they have the same number of distinct elements.For infinite sets, though, things get a bit complicated. Then it is possible for a set to be equivalent to a proper subset of itself: for example, the set of all integers is equivalent to the set of all even integers. What is required is a one-to-one mapping, f(x) = 2x, from the first set to the second.
This problem can be modeled and tested quite easily. Set A can be [X,Y], subset B [X,Y], and subset A [X,Y]. Therefore A and B are equivalent.
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.