List questions from order-theory

Published on 29 Oct 2015 - 14:48

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Prove every finite set of real numbers is well ordered.

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If a finite nonempty set of real numbers has a maximum then it has a minimum, prove.

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to prove that Inf$(B) \sqsubseteq $ Inf$(A)$.

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Width of Join Semilattice in $\mathbb R^n$

Published on 27 Mar 2026 - 15:00

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Why is this lattice modular?

Published on 31 Mar 2026 - 14:17

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Proof of Antisymmetry

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Kuratowski's closure-complement problem for the upper/lower bound functions

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For each $x,y,z∈\mathbb N$, if $x<y$ then $x+z<y+z$

Published on 23 Mar 2026 - 6:54

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For each $x,y∈\mathbb N$, if $x≤y$ and $y≤x$, then $x=y$

Published on 05 Nov 2015 - 17:54

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Field property proof

Published on 30 Mar 2026 - 0:47

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Is there a bijection $f: X \to X$ such that $f(a) \succ a$ for some $a \in X$ and $f(x) \succeq x$ for all $x \in X?$

Published on 07 Nov 2015 - 14:08

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Proving the principle of inclusion-exclusion using Möbius inversion

Published on 31 Mar 2026 - 14:46

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There is no smallest rational number greater than 2

Published on 05 Apr 2026 - 20:41

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Smallest Rational Number Proof

Published on 05 Apr 2026 - 20:40

List Question

Width of poset of posets

Prove every finite set of real numbers is well ordered.

If a finite nonempty set of real numbers has a maximum then it has a minimum, prove.

to prove that Inf$(B) \sqsubseteq $ Inf$(A)$.

Width of Join Semilattice in $\mathbb R^n$

Why is this lattice modular?

Proof of Antisymmetry

Kuratowski's closure-complement problem for the upper/lower bound functions

For each $x,y,z∈\mathbb N$, if $x<y$ then $x+z<y+z$

For each $x,y∈\mathbb N$, if $x≤y$ and $y≤x$, then $x=y$

Field property proof

Is there a bijection $f: X \to X$ such that $f(a) \succ a$ for some $a \in X$ and $f(x) \succeq x$ for all $x \in X?$

Proving the principle of inclusion-exclusion using Möbius inversion

There is no smallest rational number greater than 2

Smallest Rational Number Proof

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