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by
Ciro Santilli
(
@cirosantilli,
36
)
Axiom
Home
Mathematics
Area of mathematics
Formalization of mathematics
Formal proof
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Updated
2025-04-24
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Created
1970-01-01
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Table of contents
Consistency
Axiom
Independence (mathematical logic)
Axiom
Consistency
0
1
0
Axiom
A
set of
axioms
is consistent if they don'
t
lead
to any contradictions.
When
a
set of
axioms
is not consistent, false can be proven, and then
everything
is true, making the set of
axioms
useless.
Independence
(mathematical logic)
0
1
0
Axiom
A
theorem
is said to be independent from
a
set of
axioms
if it cannot be proven neither true nor false from those
axioms
.
It or its
negation
could therefore be arbitrarily added to the set of
axioms
.
Ancestors
(5)
Formal proof
Formalization of mathematics
Area of mathematics
Mathematics
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CIA 2010 covert communication websites
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Reuters article
Consistency
Euclid's postulates
Formalization of mathematics
Independence (mathematical logic)
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1970-01-01
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