Math 2.0

definition

Cartesian product

Definition

Let AA and BB be sets. The Cartesian product of AA and BB is the set A×B={(a,b)∣a∈A and b∈B}A \times B = \{(a, b) \mid a \in A \text{ and } b \in B\} of all ordered pairs (a,b)(a, b) with a∈Aa \in A and b∈Bb \in B.

Remarks

Example: {1,2}×{x,y}={(1,x),(1,y),(2,x),(2,y)}\{1, 2\} \times \{x, y\} = \{(1, x), (1, y), (2, x), (2, y)\}. For finite sets with mm and nn elements, A×BA \times B has mnmn elements. The plane R2\mathbb{R}^2 is R×R\mathbb{R} \times \mathbb{R}. A binary relation from AA to BB is a subset of A×BA \times B.

Explanations

L1 human

Think of a table with a row for each element of AA and a column for each element of BB. Each cell of the table is one pair (a,b)(a, b). The Cartesian product is the set of all the cells.

What this node needs for W2
  • edge instance_of in: one example (0 of 1)
  • 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/Cartesian_product, lead section

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