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Proving Natural Predecessor existence using Well Order

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#induction #natural-numbers #peano-axioms #well-orders
98
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Munkres Topology Supplementary exercises chapter 1 question 2 (a). Showing two definitions are the same

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#elementary-set-theory #well-orders
562
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How is the Continuum Hypothesis equivalent to the existence of a well-ordering on $\Bbb R$ whose bounded initial segments are countable?

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#set-theory #real-numbers #cardinals #well-orders
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
557
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Proof of the well-ordering principle

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#real-analysis #analysis #elementary-set-theory #natural-numbers #well-orders
827
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Examples of order isomorphisms / similarities between well ordered sets

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#elementary-set-theory #order-theory #well-orders
41
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Proving these sets are well-ordered with the order inherited from $\mathbb{R}$.

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#elementary-set-theory #order-theory #well-orders
40
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Munkres Topology: Section 11; Problem 3

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#general-topology #well-orders
20
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Finding the domain of a relation(transfinite recursion on a well-ordered set)

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#elementary-set-theory #well-orders
241
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Confusion in well ordering principle

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#elementary-number-theory #natural-numbers #well-orders
56
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Theorem about similarities/order-isomorphisms between well-ordered sets

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#functions #set-theory #order-theory #well-orders
97
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Ordinals and initial segments

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#set-theory #ordinals #well-orders
63
Views

Ordinal addition not commutative mistake

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#set-theory #ordinals #well-orders
62
Views

GCD / proof by induction / well founded order

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#gcd-and-lcm #euclidean-algorithm #well-orders
78
Views

Well founded orders

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#well-orders

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