Reláció

1. Sablon:Humatek Az $A$ halmazon definiált reláción az $A$-ból $A$-ba történő megfeleltetéseket értjük. Azaz egy reláció olyan speciális megfeleltetés, ahol az indulási és érkezési halmaz azonos.

• relációs jel
• határozatlansági reláció
• kongruenciareláció
• ekvivalenciareláció

• Sablon:En: Sablon:T
• Sablon:Ru: Sablon:T

• rendezés
• részbenrendezés
• lexikografikus rendezés

Basic relations:

1. equality: = → $=$
2. not equal to: \neq or \ne → $\ne$ ≠
3. less than: [[<]] → $<$
4. greater than: [[>]] → $>$
5. less than or equal to: \leq or \le → $\le$ ≤
6. greater than or equal to: \geq or \ge → $\ge$ ≥
7. approximately equal to: \approx → $\approx$ ≈
8. proportional to: \propto → $\propto$ ∝
9. congruence: \equiv → $\equiv$ ≡
10. subset of: \subset → $\subset$ ⊂
11. subset of or equal to: \subseteq → $\subseteq$ ⊆
12. superset of: \supset → $\supset$ ⊃
13. superset of or equal to: \supseteq → $\supseteq$ ⊇
14. set membership: \in → $\in$ ∈
15. not set membership: \notin → $\notin$ ∉

special relations:

1. divides: \mid → $\mid$ ∣
2. does not divide: \nmid → $\nmid$ ∤
3. parallel to: \parallel → $\parallel$ ∥
4. not parallel to: \nparallel → $\nparallel$ ∦
5. perpendicular to: \perp → $\perp$ ⟂
6. isomorphic to: \cong → $\cong$ ≅
7. equivalent to: \sim → $\sim$ ∼
8. not equivalent to: \nsim → $\nsim$ ≁
9. equivalence relation: \simeq → $\simeq$ ≃
10. asymptotically equal to: \asymp → $\asymp$ ≍

logical relations:

1. implies: \rightarrow → $\to$ →
2. if and only if: \leftrightarrow → $\leftrightarrow$ ↔
3. logical and: \land → $\wedge$ ∧
4. logical or: \lor → $\vee$ ∨

set relations:

1. element of: \in → $\in$
2. not an element of: \notin → $\notin$
3. subset: \subset → $\subset$
4. superset: \supset → $\supset$
5. subset or equal to: \subseteq → $\subseteq$
6. superset or equal to: \supseteq → $\supseteq$

miscellaneous relations:

1. proportional to: \propto → $\propto$ ∝
2. approximately equal: \approx → $\approx$ ≈
3. congruent modulo: \equiv → $\equiv$ ≡
4. union: \cup → $\cup$ ∪
5. intersection: \cap → $\cap$ ∩
6. symmetric difference: \triangle → $\mathrm{△}$ △

common poset relations:

1. less than or equal to: (partial order): \preceq → $⪯$ - this denotes the partial order relation, meaning "less than or equal to" under a given partial order.
2. strictly less than: (partial order): \prec → $\prec$ - this denotes strict inequality in a partial order, meaning that one element is strictly less than another.
3. greater than or equal to: (partial order): \succeq → $⪰$ - this is the reverse of the partial order relation, meaning "greater than or equal to."
4. strictly greater than: (partial order): \succ → $\succ$ - this denotes strict inequality in reverse, meaning one element is strictly greater than another in the partial order.
5. minimal element: for a minimal element in a poset, the relation $x⪯y$ holds for some $y$, but there is no $z$ such that $z\prec x$.
6. maximal element: for a maximal element in a poset, the relation $x⪰y$ holds for some $y$, but there is no $z$ such that $z\succ x$.

other related symbols in poset theory:

1. join least upper bound: \vee → $\vee$ - this denotes the join operation in a lattice or poset, which is the least upper bound of two elements.
2. meet greatest lower bound: \wedge → $\wedge$ - this denotes the meet operation in a lattice or poset, which is the greatest lower bound of two elements.
3. covers: (an element covers another): \lessdot → $⋖$ - this is used to indicate that one element covers another in a hasse diagram, meaning there is no element between them in the poset.
4. incomparable: \parallel → $\parallel$ - this is used to denote that two elements are incomparable in a poset, meaning neither $x⪯y$ nor $y⪯x$ holds.
5. non-comparable relation: \npreceq → $⋠$ - this indicates that the element is not "less than or equal to" in the poset.