From 5b6a542e64da7ca784c84d70f260e89e4e272b95 Mon Sep 17 00:00:00 2001 From: denes-sebestyen <163525320+denes-sebestyen@users.noreply.github.com> Date: Sat, 4 Jan 2025 17:28:22 +0100 Subject: [PATCH] =?UTF-8?q?4.=20t=C3=A9tel=20-=20r=C3=A9szhalmaz=20definic?= =?UTF-8?q?=C3=B3=20jav=C3=ADt=C3=A1sa=20(#16)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../4. Számelmélet, gráfok.pdf | Bin 256599 -> 257898 bytes .../4. Számelmélet, gráfok.tex | 4 ++-- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/4. Számelmélet, gráfok, (Kódoláselmélet)/4. Számelmélet, gráfok.pdf b/4. Számelmélet, gráfok, (Kódoláselmélet)/4. 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Számelmélet, gráfok, (Kódoláselmélet)/4. Számelmélet, gráfok.tex b/4. Számelmélet, gráfok, (Kódoláselmélet)/4. Számelmélet, gráfok.tex index 9b6b51c..96b4229 100644 --- a/4. Számelmélet, gráfok, (Kódoláselmélet)/4. Számelmélet, gráfok.tex +++ b/4. Számelmélet, gráfok, (Kódoláselmélet)/4. Számelmélet, gráfok.tex @@ -46,8 +46,8 @@ A halmaz (rendszer, osztály, összesség, ...) elemeinek gondolati burka. Egy h \item Üres halmaz \\ Az a halmaz, amelynek nincs eleme az Üres halmaz. Jele: $\emptyset$ . A meghatározottsági axióma alapján ez egyértelmű \item Részhalmaz \\ - $(x,y)$ rendezett pár, ha $(x,y) = (u,v) \Longleftrightarrow x = u \ \land \ y = v$. Ezt a tulajdonságot halmazokkal definiáljuk: - \[ (x,y) := \{ \{x\}, \{x, y\} \} \] + Azt mondjuk, hogy \textbf{A részhalmaza B-nek} ($A \subseteq B$), ha $\forall a \in A : a \in B$, azaz A minden elemét tartalmazza B. + \textbf{A valódi részhalmaza B-nek} \(A \subset B\), ha $A \subseteq B$, de $A \neq B$, azaz B-nek van legalább egy olyan eleme, ami nem eleme A-nak. \item Hatvány halmaz \\ Ha {\it A} egy halmaz, akkor azt a halmazrendszert, melynek elemei pontosan az {\it A} halmaz részhalmazai az {\it A} hatványhalmazának mondjuk, és $2^A$-val jelöljük. \begin{itemize}