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Axioms
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The fundamental axioms of mathematics
September 4th, 2020
foundations
axioms
logic
Why is matrix multiplication defined a certain way?
July 8th, 2020
matrices
axioms
Proofs using the Axioms of Probability
August 1st, 2022
axioms
probability
Is it possible to have a field without an additive identity?
August 1st, 2022
axioms
field-theory
Axiom of Pairing
August 1st, 2022
elementary-set-theory
axioms
Is the parallelogram law a theorem or an axiom?
August 1st, 2022
axioms
What does it mean to axiomatize a logic?
August 1st, 2022
predicate-logic
axioms
logic
Describe a sound and complete proof system
August 1st, 2022
logic
axioms
prove that if $a=b$ then $a+c=b+c$ where $a,b,c\in \mathbb R$
August 1st, 2022
equivalence-relations
real-numbers
relations
field-theory
axioms
A set is not an element of itself.
August 1st, 2022
elementary-set-theory
axioms
What is the definition of axiom (mathematically speaking)
August 1st, 2022
axioms
definition
Two congruent segments does have the same length?
January 12th, 2020
congruence-relations
geometry
axioms
Is the axiom schema of specification sufficient for solving Russell's paradox? If so, why?
August 1st, 2022
axioms
elementary-set-theory
paradoxes
Can multiplication be defined without addition?
August 1st, 2022
arithmetic
axioms
definition
Prove addition is commutative using axioms, definitions, and induction
March 5th, 2020
natural-numbers
real-analysis
proof-verification
axioms
peano-axioms
How do we define arc length?
August 1st, 2022
geometry
proof-verification
definition
circles
axioms
Proof: Zero is less than one
August 1st, 2022
field-theory
axioms
How do you formally state the axiom of constructibility?
August 1st, 2022
set-theory
axioms
Axiomatic definition of the real numbers and uncountability
November 15th, 2020
logic
real-numbers
axioms
What is the rule for something divided by itself equaling 1?
August 1st, 2022
axioms
Why does this proof that Every Well-ordered Set is Isomorphic to a Unique Ordinal need to use the Axiom of Replacement
August 1st, 2022
ordinals
well-orders
axioms
set-theory
What are the primitive notions of real analysis?
August 1st, 2022
definition
real-analysis
axioms
What's the differences between naive and axiomatic set theory?
June 25th, 2020
set-theory
axioms
Is axiom of completeness an axiom?
August 1st, 2022
real-analysis
axioms
Need help understanding Axiom of Extensionality
August 1st, 2022
axioms
elementary-set-theory
Derive by modus ponens $[A\rightarrow(B\rightarrow C)]\rightarrow[(A\rightarrow B)\rightarrow(A\rightarrow C)]$
April 30th, 2020
propositional-calculus
axioms
nonclassical-logic
logic
Using field axioms for a simple proof
August 1st, 2022
axioms
field-theory
Problem understanding the Axiom of Foundation
August 1st, 2022
axioms
set-theory
axioms of equality
August 1st, 2022
axioms
logic
set-theory
Problems with axioms
August 1st, 2022
axioms
calculus
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