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How to apply Zorn's Lemma to prove cardinalities are a total order?

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#elementary-set-theory #order-theory #axiom-of-choice #transfinite-induction
130
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using strong induction that there exists an integer $C$ that for all $D\ge C$ it is possible to return exactly $D$ by using only $2$ and $5$

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#discrete-mathematics #induction #transfinite-induction
80
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What do we call a function that converges with composition over greater than $\omega$ times?

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#convergence-divergence #induction #ordinals #transfinite-induction
56
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Ordinal equation

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#set-theory #ordinals #transfinite-induction
294
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Trying to prove that cardinality of Borel $\sigma$-algebra is the cardinality of the continuum

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#measure-theory #set-theory #solution-verification #borel-sets #transfinite-induction
687
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Does every partial order admit a maximal chain?

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#proof-writing #set-theory #order-theory #axiom-of-choice #transfinite-induction
156
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CH implies $\omega_1$ pairwise disjoint of perfect set

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#set-theory #descriptive-set-theory #transfinite-induction
86
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How can I write a perfect set as $c$ many pairwise disjoint perfect sets

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#set-theory #descriptive-set-theory #transfinite-recursion #transfinite-induction
180
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$\Delta$-system lemma to show ccc

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#set-theory #forcing #transfinite-induction
201
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Continuous function with some properties plus everywhere surjective function must be everywhere surjective

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#set-theory #transfinite-recursion #transfinite-induction
94
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Using transfinite induction to split $R$ to continuum many pairwise disjoint subsets of $R$

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#set-theory #transfinite-recursion #transfinite-induction
61
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Question regarding initial segment and transfinite induction.

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#induction #set-theory #order-theory #well-orders #transfinite-induction
217
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Proving the cardinality of B<A (Terence Tao's Analysis I book Ex 8.5.15)

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#analysis #logic #transfinite-recursion #transfinite-induction
359
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Disparity between Induction and Well-ordering Principles

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#logic #induction #first-order-logic #well-orders #transfinite-induction
253
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Transfinite induction

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#logic #induction #set-theory #transfinite-induction

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