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Status: Tags: Links: Discrete Math Rules

Rule of Universal Generalization

Definition

• If an open statement P(x) is proved to be true when x is assigned by any arbitrary chosen (generic) value from the universe, then the statement ∀x P(x) is also true.

Example

• Prove If 2x-6=0, then x=3
• Proof
  • Take any number c such that 2c-6=0
    • 2c=6, c=3
    • Since c is an arbitrary number, theorem is proved
• In the first number we consider a generic value (any number c)
  • No specific properties, not other value in universe
  • Since value is proved with a generic value, it will work for any specific
• Arbitrary rules

Backlinks

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list from Rule of Universal Generalization AND !outgoing(Rule of Universal Generalization)

References:

Created:: 2021-10-07 09:01