axiom schema उदाहरण वाक्य

This axiom schema was tacitly used in the early days of naive set theory, before a strict axiomatization was adopted.
"' Strong collection schema "': This is the constructive replacement for the axiom schema of replacement.
Each of these patterns is an " axiom schema ", a rule for generating an infinite number of axioms.
In other words, if the relation \ phi represents a definable function f, A represents its axiom schema of collection.
An inference rule containing no premises is called an axiom schema or, if it contains no metavariables, simply an axiom.

Such an axiom schema allows infinitely many axioms having a common form to be written as a finite expression connoting that form.
Note that adopting this as an axiom schema will not replace the axiom of union, which is still needed for other situations.
Because the axiom schema of separation is not independent, it is sometimes omitted from contemporary statements of the Zermelo-Fraenkel axioms.
Thus the laws listed below are actually axiom schemas, that is, they stand in place of an infinite number of instances.
The formal version of this axiom resembles the axiom schema of replacement, and embodies the class function " F ".