What does axiom schema of replacement mean?
Definitions for axiom schema of replacement
ax·iom schema of re·place·ment
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Wikipedia
Axiom schema of replacement
In set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZF) that asserts that the image of any set under any definable mapping is also a set. It is necessary for the construction of certain infinite sets in ZF. The axiom schema is motivated by the idea that whether a class is a set depends only on the cardinality of the class, not on the rank of its elements. Thus, if one class is "small enough" to be a set, and there is a surjection from that class to a second class, the axiom states that the second class is also a set. However, because ZFC only speaks of sets, not proper classes, the schema is stated only for definable surjections, which are identified with their defining formulas.
Numerology
Chaldean Numerology
The numerical value of axiom schema of replacement in Chaldean Numerology is: 9
Pythagorean Numerology
The numerical value of axiom schema of replacement in Pythagorean Numerology is: 1
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"axiom schema of replacement." Definitions.net. STANDS4 LLC, 2024. Web. 27 Apr. 2024. <https://www.definitions.net/definition/axiom+schema+of+replacement>.
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