Multiset facts for kids
A multiset is a special kind of collection in mathematics. It's a lot like a set, where you gather different items together. But there's one big difference: in a multiset, you can have the same item appear more than once!
Think of it like a bag of marbles. If you have a set of marbles, you might say you have {red, blue, green}. But if you have a multiset, you could have {red, red, blue, green, green, green}.
Mathematicians use a special word called multiplicity to say how many times an item appears in a multiset. For example, in the multiset { a, a, b, b, b, c }:
- The item a has a multiplicity of 2 (it appears 2 times).
- The item b has a multiplicity of 3 (it appears 3 times).
- The item c has a multiplicity of 1 (it appears 1 time).
Multisets can be shown using a histogram, which is a type of bar graph.
It's helpful to compare multisets with tuples and sets:
- In a tuple, the order of items matters, and items can be repeated. So, (a,b) is different from (b,a), and (a,a) is different from (a).
- In a multiset, the order doesn't matter, but items can be repeated. So, {a,b} is the same as {b,a}, but {a,a} is different from {a}.
- In a set, the order doesn't matter, and items cannot be repeated. So, {a,b} is the same as {b,a}, and {a,a} is the same as {a}.
Examples of Multisets
Prime Factors
One common example of a multiset is the collection of prime factors of a number. Prime factors are the prime numbers that multiply together to make a certain number.
Let's take the number 120. Its prime factorization is:
- 120 = 2 × 2 × 2 × 3 × 5
So, the multiset of prime factors for 120 is {2, 2, 2, 3, 5}. Notice how the number 2 appears three times.
Solutions to Equations
Another example comes from algebra when solving equations. An algebraic equation can have several solutions. Sometimes, these solutions can be the same number.
For instance, a quadratic equation usually has two solutions.
- If you solve an equation and get the solutions 3 and 5, the multiset of solutions is {3, 5}.
- But if you solve another equation and both solutions turn out to be 4, then the multiset of solutions is {4, 4}. In this case, the solution 4 has a multiplicity of 2.
Related topics
See also
In Spanish: Multiconjunto para niños
