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Prove the distributive law $a(b+c)=ab+ac$ for real numbers?

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#algebra-precalculus #axioms
243
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Help needed with axiomatic deductions

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#predicate-logic #axioms #first-order-logic
258
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Well-Ordering Theorem without Axiom of Regularity

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#set-theory #axioms
341
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Is $\mathrm{ZFC}^E$ outright inconsistent?

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#set-theory #axioms
577
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How can I define $\mathbb{N}$ if I postulate existence of a Dedekind-infinite set rather than existence of an inductive set?

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#set-theory #infinity #axioms #natural-numbers
418
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Difference between impredicative and predicative version of separation axiom

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#set-theory #philosophy #axioms
521
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Equivalent formulations of the Axiom of Replacement

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#set-theory #axioms
274
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Meaning of the Axiom of regularity (foundation)

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#set-theory #axioms
233
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Let $F$ be a field and $x, y\in F$. Prove:

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#proof-writing #axioms
339
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Simple Proofs in ZFC Set Theory

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#elementary-set-theory #proof-writing #axioms
70
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Are there any formal theories that are not axiomatic?

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#axioms #formal-systems
374
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Does every mathematical principle have a proof?

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#logic #terminology #axioms #foundations
477
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Topology: Opens vs Neighborhoods

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#general-topology #continuity #definition #axioms
1.5k
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Axiom of Pairing

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#elementary-set-theory #axioms
62
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A problem in transitivity of set

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#set-theory #axioms

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