relation

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relation (tsz. relations)

1. viszony
2. (matematika) reláció

Basic relations:

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

special relations:

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

logical relations:

1. implies: \rightarrow → ${\textstyle \rightarrow }$ →
2. if and only if: \leftrightarrow → ${\textstyle \leftrightarrow }$ ↔
3. logical and: \land → ${\textstyle \land }$ ∧
4. logical or: \lor → ${\textstyle \lor }$ ∨

set relations:

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

miscellaneous relations:

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

common poset relations:

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

other related symbols in poset theory:

1. join least upper bound: \vee → ${\textstyle \vee }$ - 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 → ${\textstyle \wedge }$ - 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 → ${\textstyle \lessdot }$ - 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 → ${\textstyle \parallel }$ - this is used to denote that two elements are incomparable in a poset, meaning neither ${\textstyle x\preceq y}$ nor ${\textstyle y\preceq x}$ holds.
5. non-comparable relation: \npreceq → ${\textstyle \npreceq }$ - this indicates that the element is not "less than or equal to" in the poset.

További információk

• relation - Szótár.net (en-hu)
• relation - Sztaki (en-hu)
• relation - Merriam–Webster
• relation - Cambridge
• relation - WordNet
• relation - Яндекс (en-ru)
• relation - Google (en-hu)
• relation - Wikidata
• relation - Wikipédia (angol)