Math 2.0

definition

Set

Definition

A set is a collection of objects, called the elements of the set. For an object xx and a set AA, either xx is an element of AA, written x∈Ax \in A, or it is not, written x∉Ax \notin A. Two sets AA and BB are equal when they have the same elements: for each xx, x∈Ax \in A if and only if x∈Bx \in B. A finite set can be written by a list of its elements in braces, for example {1,2,3}\{1, 2, 3\}.

Remarks

The sets {1,2,3}\{1, 2, 3\}, {3,2,1}\{3, 2, 1\} and {1,1,2,3}\{1, 1, 2, 3\} are the same set. In Zermelo–Fraenkel set theory, "set" and "∈\in" are primitive notions, and the axioms say how they behave. Not every collection can be a set. Russell's paradox shows this.

Explanations

L1 human

A set is like a bag of objects, where only membership counts. The bag {1,2,3}\{1, 2, 3\} contains 11, 22 and 33, and nothing else. You cannot put the same object in twice, and the objects have no order.

What this node needs for W2
  • edge not_instance_of in: one non-example that fails one clause (0 of 1)

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Sources

  1. Web https://en.wikipedia.org/wiki/Set_(mathematics), lead section

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