Latex - mnoziny, mnozinove operacie

[Martin Sleziak]

Pri mnozinovych zatvorkach treba pouzivat backslash. Patri sa oznacuje \in

$\{x\cdot y; y\in H\}$, $\mathbb N=\{0,1,2,3,\dots\}$

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\{x\cdot y; y\in H\}, \mathbb N=\{0,1,2,3,\dots\}

Podmnozina

$A\subset B$, $A\subseteq B$, $A\subsetneq B$

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A\subset B, A\subseteq B, A\subsetneq B

Zakladne operacie s mnozinami

$A\cup B$, $A\cap B$ $A\setminus B$

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A\cup B, A\cap B A\setminus B

Zjednotenie a prienik mozeme robit aj so sytemami mnozin:

$\bigcup_{i=1}^\infty \bigcap_{j=1}^\infty A_{ij}$

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\bigcup_{i=1}^\infty \bigcap_{j=1}^\infty A_{ij}

Pokial chceme rozsah nad a pod znak prieniku a zjednotenia
$\bigcup\limits_{i=1}^\infty \bigcap\limits_{j=1}^\infty A_{ij}$

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\bigcup\limits_{i=1}^\infty \bigcap\limits_{j=1}^\infty A_{ij}

Na uzavrete intervaly sa pouziva langle rangle, nie < a >. (Niektori ludia preferuju hranate zatvorky na oznacenie intervalu - $[0,1]$
$(0,1)\subseteq (0,1\rangle \subseteq \langle 0,1\rangle$

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(0,1)\subseteq (0,1\rangle \subseteq \langle 0,1\rangle

V suvislosti s mnozinami (napriklad pri definiciach mnozinovych operacii), sa vyskytuju aj kvantifikatory a logicke spojky; tie najdete tu.

Pri oznacovani kardinality sa stretnete s pismenom alef:
$\aleph_0 < \aleph_1 \le 2^{\aleph_0}$

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\aleph_0 < \aleph_1 \le 2^{\aleph_0}

Alebo tiez s kardinalitou kontinua:
$2^{\aleph_0}=\mathfrak c$

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$2^{\aleph_0}=\mathfrak c$

[Martin Sleziak]

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$f\colon X\to Y$ alebo $f:X\to Y$

$f\colon X\to Y$ alebo $f:X\to Y$

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$x\mapsto x^2$

$x\mapsto x^2$

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$g\circ f(x)=g(f(x))$ a $h\circ (g\circ f)=(h\circ g)\circ f$

$g\circ f(x)=g(f(x))$ a $h\circ (g\circ f)=(h\circ g)\circ f$