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Initial segment of a well-ordered set

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#well-orders
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Order of ordinal numbers

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#set-theory #well-orders
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Multplication of well ordered sets is not commutative

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#order-theory #well-orders
149
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Well-Ordering Proof in Cunningham

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#set-theory #proof-explanation #order-theory #well-orders
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What order types can well-ordered proper classes have?

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#logic #set-theory #ordinals #well-orders #second-order-logic
60
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Addition in $\mathbb{R}$ preserves order

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#elementary-set-theory #real-numbers #well-orders
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Characterization of the least fixed point of a function$\pi$ on $\mathcal{P}(A)$ where $\pi(X) := \{y \in A | (\forall x<y)[x \in X] \}$

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#fixed-point-theorems #well-orders #fixed-points
152
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Proof of the principle of well-ordered induction in the book of Rosen's Discrete Mathematics

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#discrete-mathematics #induction #well-orders
93
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If A is a finite set $\implies$ <A,R> and $<A,R^{-1}>$ are well ordered sets.

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#discrete-mathematics #elementary-set-theory #well-orders
27
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The Hartogs operation is monotone

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#elementary-set-theory #well-orders
55
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How many subsets of a well ordered set are isomorphic to the whole set?

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#elementary-set-theory #well-orders
61
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Proof of Induction on Formulas using well ordering principle

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#logic #well-orders
36
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Well ordering of $\mathbb{N}$ with weak induction

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#abstract-algebra #induction #order-theory #natural-numbers #well-orders
136
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Why is (ℕ, $\leq$) considered a well ordered set but (ℕ, $\geq$) is not?

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#discrete-mathematics #relations #well-orders
84
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Mathematics for Computer Science Prob. 2.6 Well Ordering Principle

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#discrete-mathematics #proof-writing #solution-verification #well-orders

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