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A couple of well ordering proofs.

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#set-theory #ordinals #well-orders
43
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Using WOP to prove certain naturals can be written a certain way.

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#elementary-set-theory #proof-writing #well-orders
48
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If i have an a well ordered set in which every chain admits an upper bound then the maximal element is unique

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#order-theory #well-orders
111
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Intuitionistic well-orderings of uncountable sets

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#constructive-mathematics #well-orders #intuitionistic-logic
117
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a proof idea: Every well-ordered set has an order-preserving bijection to exactly one ordinal.

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#logic #solution-verification #set-theory #ordinals #well-orders
343
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Difference between partially ordered, totally ordered, and well ordered sets.

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#elementary-set-theory #relations #order-theory #well-orders
46
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Limit Countable Ordinal - is it a limit of a intuitive sequence of ordinals?

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#elementary-set-theory #set-theory #order-theory #ordinals #well-orders
126
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Prove that if $A$ is any well-ordered set of real numbers and $B$ is a nonempty subset of $A$, then $B$ is well-ordered.

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#elementary-set-theory #well-orders
124
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Well-ordering theorem and cardinality of real numbers

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#set-theory #axiom-of-choice #well-orders
50
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Using the Principle of Well Order, show that for all $n \in N$ it holds that $4^n -1$ is divisible by 3.

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#discrete-mathematics #well-orders #theorem-provers
106
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What does the cardinality alone of a totally ordered set say about the ordinals that can be mapped strictly monotonically to it?

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#set-theory #order-theory #cardinals #ordinals #well-orders
102
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Why does proof of Zorn's lemma need to use the fact about ordinals being too large to be a set?

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#set-theory #axiom-of-choice #ordinals #well-orders #transfinite-recursion
136
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Can every statement that can be proved using the well-ordering principle be proved using weak mathematical induction?

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#discrete-mathematics #logic #proof-writing #induction #well-orders
43
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If $X_1$,$X_2$ are wosets isomorphic to ordinals $\alpha_1,\alpha_2$ then $X_1\times X_2$ is isomorphic to $\alpha_2\cdot \alpha_1$

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#solution-verification #ordinals #well-orders #transfinite-induction
102
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Prove that $\mathbb N \times \mathbb N$ is well ordered under $\le$

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#proof-writing #set-theory #natural-numbers #well-orders

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