ideal$37298$ - traduzione in greco
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ideal$37298$ - traduzione in greco

FAMILY CLOSED UNDER SUBSETS AND COUNTABLE UNIONS
Σ-ideal; S-ideal; Sigma ideal

ideal      
n. ιδανικό
mechanical advantage         
  • Two meshing gears transmit rotational motion.
MEASURE OF THE FORCE AMPLIFICATION ACHIEVED BY USING A TOOL, MECHANICAL DEVICE OR MACHINE SYSTEM
Actual mechanical advantage; Ideal mechanical advantage; Mechanical Powers; Mechanical powers; Force ratio; Ideal Mechanical Advantage
μηχανικό όφελος
logic gate         
  • A synchronous 4-bit up/down decade counter symbol (74LS192) in accordance with ANSI/IEEE Std. 91-1984 and IEC Publication 60617-12.
  • AND symbol
  • AND symbol
  • Buffer symbol
  • Buffer symbol
  • [[CMOS]] diagram of a [[NOT gate]], also known as an inverter. [[MOSFET]]s are the most common way to make logic gates.
  • NAND symbol
  • NAND symbol
  • NOR symbol
  • NOR symbol
  • NOT symbol
  • NOT symbol
  • OR symbol
  • OR symbol
  • Animation of how an SR [[NOR gate]] latch works.
  • The 7400 chip, containing four NANDs. The two additional pins supply power (+5 V) and connect the ground.
  • A tristate buffer can be thought of as a switch. If ''B'' is on, the switch is closed. If B is off, the switch is open.
  • XNOR symbol
  • XNOR symbol
  • XOR symbol
  • XOR symbol
COMPUTATIONAL EQUIPMENT, PHYSICAL OR THEORETICAL, THAT PERFORMS A BOOLEAN LOGIC FUNCTION
Logic Gate; Logic circuit; Discrete logic; Logic gates; Digital logic; Binary logic elements; Digital Logic; Logical gate; Logic circuits; Logic device; Electronic gate; Bubble pushing; Universal Logic Gate; Universal logic gate; Electronic logic gates; Electronic logic gate; Ideal logic gate; Logical circuit; Gates on chips
λογική πύλη

Definizione

ideal
<theory> In domain theory, a non-empty, downward closed subset which is also closed under binary least upper bounds. I.e. anything less than an element is also an element and the least upper bound of any two elements is also an element. (1997-09-26)

Wikipedia

Sigma-ideal

In mathematics, particularly measure theory, a 𝜎-ideal, or sigma ideal, of a sigma-algebra (𝜎, read "sigma," means countable in this context) is a subset with certain desirable closure properties. It is a special type of ideal. Its most frequent application is in probability theory.

Let ( X , Σ ) {\displaystyle (X,\Sigma )} be a measurable space (meaning Σ {\displaystyle \Sigma } is a 𝜎-algebra of subsets of X {\displaystyle X} ). A subset N {\displaystyle N} of Σ {\displaystyle \Sigma } is a 𝜎-ideal if the following properties are satisfied:

  1. N {\displaystyle \varnothing \in N} ;
  2. When A N {\displaystyle A\in N} and B Σ {\displaystyle B\in \Sigma } then B A {\displaystyle B\subseteq A} implies B N {\displaystyle B\in N} ;
  3. If { A n } n N N {\displaystyle \left\{A_{n}\right\}_{n\in \mathbb {N} }\subseteq N} then n N A n N . {\textstyle \bigcup _{n\in \mathbb {N} }A_{n}\in N.}

Briefly, a sigma-ideal must contain the empty set and contain subsets and countable unions of its elements. The concept of 𝜎-ideal is dual to that of a countably complete (𝜎-) filter.

If a measure μ {\displaystyle \mu } is given on ( X , Σ ) , {\displaystyle (X,\Sigma ),} the set of μ {\displaystyle \mu } -negligible sets ( S Σ {\displaystyle S\in \Sigma } such that μ ( S ) = 0 {\displaystyle \mu (S)=0} ) is a 𝜎-ideal.

The notion can be generalized to preorders ( P , , 0 ) {\displaystyle (P,\leq ,0)} with a bottom element 0 {\displaystyle 0} as follows: I {\displaystyle I} is a 𝜎-ideal of P {\displaystyle P} just when

(i') 0 I , {\displaystyle 0\in I,}

(ii') x y  and  y I {\displaystyle x\leq y{\text{ and }}y\in I} implies x I , {\displaystyle x\in I,} and

(iii') given a sequence x 1 , x 2 , I , {\displaystyle x_{1},x_{2},\ldots \in I,} there exists some y I {\displaystyle y\in I} such that x n y {\displaystyle x_{n}\leq y} for each y . {\displaystyle y.}

Thus I {\displaystyle I} contains the bottom element, is downward closed, and satisfies a countable analogue of the property of being upwards directed.

A 𝜎-ideal of a set X {\displaystyle X} is a 𝜎-ideal of the power set of X . {\displaystyle X.} That is, when no 𝜎-algebra is specified, then one simply takes the full power set of the underlying set. For example, the meager subsets of a topological space are those in the 𝜎-ideal generated by the collection of closed subsets with empty interior.