Math 2.0

definition

Predicate

Definition

Let XX be a set. A predicate on XX is a statement P(x)P(x) with a variable xx that ranges over XX, such that P(a)P(a) is a proposition for each a∈Xa \in X. More generally, a predicate P(x1,…,xn)P(x_1, \dots, x_n) has nn variables, and nn is its arity.

Remarks

The predicate "x>3x > 3" on the integers gives the true proposition "5>35 > 3" and the false proposition "1>31 > 3". A predicate on XX determines the set {x∈X∣P(x)}\{x \in X \mid P(x)\} of the values that make it true. See set-builder notation. A predicate with two variables is a binary relation.

Explanations

L1 human

A predicate is a sentence with a blank, such as "___ is prime". It is not true or false yet. When you fill the blank with a number, you get a proposition.

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)

The writing levels say how complete the text of a node is. They do not measure its truth.

What this needs

To read this node, read these 2 nodes in this order. The foundations come first, and the list ends with this node.

Proposition, concept, no evidence levelPropositionconceptPredicate, definition, no evidence levelPredicatedefinition
Each node uses the nodes above it. The colour of the bar on a box shows the evidence level, and the box also gives it as text. The list below has the same nodes.
  • no evidence level
  1. Proposition concept
  2. Predicate definition

What depends on this

438 nodes use this node, directly or through other nodes.

Sources

  1. Web https://en.wikipedia.org/wiki/Predicate_(logic), lead section

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