Collections

Inajengwa juu ya

Hakuna masharti ya awali — anza hapa!

Utajifunza

• Sort objects into collections using a stated rule, and describe the rule someone else used.
• Decide whether a given object is a member of a collection.
• Explain that two collections are the same exactly when they have the same members, however they are arranged or listed.
• Recognise the empty collection and count the members of small collections.

Fasili

• A collection is a group of things considered together; the things in it are its members.
• Two collections are equal when every member of each one is also a member of the other.
• The empty collection is the collection with no members.
• Sorting (classification) places objects into collections according to a rule, such as colour or shape.

Nadharia

• Rearranging the members, or listing them in a different order, does not change a collection.
• Naming the same member twice does not add a new member.
• Counting the members of a collection gives the same answer whatever order we count them in.
• There is only one empty collection: any two collections with no members have exactly the same members.

Mawazo potofu ya kawaida

• Thinking a collection changes when its members are moved around or listed in a different order.
• Believing that a collection with nothing in it is not a collection at all.
• Confusing a box that contains an empty box with an empty box: the first one has one member.
• Thinking an object can belong to only one collection (the same toy can be in 'red things' and in 'round things').

Inaelekea kwa

Ugunduzi wa hiari

• Russell's paradox and why sets need axioms A collection can itself be a member of another collection, like a box inside a box. Pushing this to 'the collection of all collections that are not members of themselves' leads to Russell's paradox.Njia ya Maajabu →
• Relations, equivalence relations and partitions Sorting by a rule so that every object lands in exactly one group is the seed of a partition; partitions correspond exactly to equivalence relations.

Njia za kujifunza

• Conventional K–12 progression

Usomaji zaidi

• Paul R. Halmos, Naive Set Theory (1960) — Background for educators, not for children.