92
Líon torthaí a aimsíodh
Number of matches found
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Mathematics » Logic & Set Theory An axiom is an initial proposition which is assumed to be true.
Matamaitic » Loighic & Tacartheoiric Is éard is aicsím ann ná buntairiscint a nglactar leis go bhfuil sí fíor.
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Mathematics » Logic & Set Theory An infinite set, the members of which are countable e.g. the set of natural numbers or the set of integers are both countably infinite sets but the set of all real numbers or the set of all rational numbers are not.
Matamaitic » Loighic & Tacartheoiric Tacar éigríochta, gur féidir a bhaill a chomhaireamh e.g. is tacair éigríochta inchomhairthe iad tacar na n-uimhreacha aiceanta agus tacar na slánuimhreacha ach ní hea tacar na réaduimhreacha uile ná tacar na n-uimhreacha cóimheasta uile.
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Mathematics » Logic & Set Theory The difference (or relative complement) of the sets A and B is the set of those elements of A which do not belong to B.
Matamaitic » Loighic & Tacartheoiric Is ionann an difríocht (nó an comhlánú coibhneasta) idir na tacair A agus B agus tacar na mball sin de A nach bhfuil i B.
FÉACH FREISIN · SEE ALSO
# relative complement of two sets · comhlánú coibhneasta dhá thacar#
Mathematics » Logic & Set Theory Two (or more) sets are disjoint if they have no common element. Their intersection is identical to the null or empty set.
Matamaitic » Loighic & Tacartheoiric Bíonn dhá thacar (nó breis) scartha mura mbíonn aon bhall coiteann iontu. Is comhionann a n-idirmhír agus an tacar neamhnitheach nó folamh.
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Mathematics » Logic & Set Theory The disjunction of two propositions p and q is the logical OR of p and q. (Databases) The creation of one relation from two relations, which is composed of every tuple of either one of the two relations, or of both.
Matamaitic » Loighic & Tacartheoiric Is ionann aontas dhá thairiscint p agus q agus NÓ loighciúil p agus q. (Bunachair shonraí) Gaol amháin a chruthú ó dhá ghaol, atá comhdhéanta de gach uile chodach i gceachtar den dá chodach nó sa dá cheann.
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The name given to an item in a set. (Computing) 1. An object, entity, or concept having the properties that define a set. 2. A parameter value in a list of parameter values. 3. The smallest unit of data in a table or array. . (Logic) The relationship between an element and a set indicated by the statement x is an element of the set X and written as x ∈ X. This is taken as an undefined relationship.
An t-ainm a thugtar ar mhír de thacar. (Ríomhaireacht) 1. Aidhm, aonán nó coincheap a bhfuil na hairíonna aige/aici atá sainiúil do thacar. 2. Luach paraiméadair i liosta luachanna paraiméadar. 3. An t-aonad is lú sonraí i dtábla nó in eagar. 4. (Loighic) An gaol idir ball agus tacar a léirítear sa ráiteas is ball den tacar X é x agus a scríobhtar mar x ∈ X. Glactar leis gur gaol neamhshainithe é seo.
x is an element of the set y
is ball den tacar y é x
tá x ina bhall den tacar y
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Mathematics » Logic & Set Theory An element x which is a member of the universal set, is an element of the truth set of an open sentence if and only if its substitution results in a true proposition.
Matamaitic » Loighic & Tacartheoiric Chun gur ball de thacar fírinne abairte oscailte é ball x atá ina bhall den uilethacar is gá agus is leor gur tairiscint fhíor atá mar thoradh ar é a chur in ionad na hathróige.
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Mathematics » Logic & Set Theory The set with no elements.
Matamaitic » Loighic & Tacartheoiric Tacar gan aon bhaill.
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The relation equality is an equivalence relation as it has the properties: 1. a = a 2. if a = b then b = a 3. if a = b and if b = c, then a = c.
Is gaol coibhéise é coibhneas na cothroime ó tá na hairíonna seo aige: 1. a = a 2. má tá a = b ansin tá b = a 3. má tá a = b agus má tá b = c, ansin tá a = c.
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Mathematics » Logic & Set Theory Two formulae r and s are called equivalent if and only if the truth value of r is equal to the truth value of s for each choice of propositions which are substituted for their respective variables.
Matamaitic » Loighic & Tacartheoiric Deirtear go bhfuil dhá fhoirmle r agus s coibhéiseach más gá agus más leor luach fírinne r a bheith cothrom le luach fírinne s do gach aon rogha de thairiscintí a chuirtear in ionad a n-athróg faoi seach.
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Mathematics » Logic & Set Theory Two open sentences are said to be equivalent if and only if their truth sets are identical.
Matamaitic » Loighic & Tacartheoiric Deirtear go bhfuil dhá abairt oscailte coibhéiseach más gá agus más leor a dtacair fhírinne a bheith comhionann.
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Mathematics » Logic & Set Theory Two propositions are said to be equivalent if they have the same truth values. (cf. equivalence relation).
Matamaitic » Loighic & Tacartheoiric Deirtear go bhfuil dhá thairiscint coibhéiseach más ionann a luachanna fírinne. (fch. gaol coibhéise)
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Mathematics » Logic & Set Theory A relation a * b between two mathematical entities is an equivalence relation if and only if it has the properties: 1. a * a 2. if a * b then b * a 3. if a * b and if b * c, then a * c.
Matamaitic » Loighic & Tacartheoiric Is ionann gaol a * b idir dhá aonán mhatamaiticiúla agus gaol coibhéise más gá agus más leor go bhfuil na hairíonna seo aige: 1. a * a 2. má tá a * b ansin tá b * a 3. má tá a * b agus má tá b * c, ansin tá a * c.
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there exists x such that
is ann do x ionas go bhfuil
There exists an interval such that f(I)=[a,b].
Is ann d'eatramh ionas go bhfuil f(I)=[a,b].
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Mathematics » Logic & Set Theory A set with a finite number of elements.
Matamaitic » Loighic & Tacartheoiric Tacar a bhfuil líon críochta de bhaill ann.
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Mathematics » Logic & Set Theory The quantifier for all. This is used to indicate that an open sentence is true (or false) for all members of the set e.g. for all x such that x is a human being, x is mortal.
Matamaitic » Loighic & Tacartheoiric An cainníochtóir do gach. Úsáidtear é seo chun a léiriú go bhfuil abairt oscailte fíor (nó bréagach) do gach ball den tacar e.g. do gach x ionas gur duine daonna é x, tá x básmhar.
FÉACH FREISIN · SEE ALSO
# for every... · do gach...#
Mathematics » Logic & Set Theory The quantifier for any. This is used to indicate that an open sentence is true (or false) for any member of the set e.g. for any x such that x is a human being, x is mortal.
Matamaitic » Loighic & Tacartheoiric An cainníochtóir d'aon. Úsáidtear é seo chun a léiriú go bhfuil abairt oscailte fíor (nó bréagach) d'aon bhall den tacar e.g. d'aon x ionas gur duine daonna é x, tá x básmhar.
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Mathematics » Logic & Set Theory The quantifier for every. This is used to indicate that an open sentence is true (or false) for every member of the set e.g. for every x such that x is a human being, x is mortal.
Matamaitic » Loighic & Tacartheoiric An cainníochtóir do gach. Úsáidtear é seo chun a léiriú go bhfuil abairt oscailte fíor (nó bréagach) do gach ball den tacar e.g. do gach x ionas gur duine daonna é x, tá x básmhar.
FÉACH FREISIN · SEE ALSO
# for all... · do gach...#
Mathematics » Logic & Set Theory General theorems express relationships which are true for all members of the stated set of objects, such as: The base angles of an isosceles triangle are equal.
Matamaitic » Loighic & Tacartheoiric Cuireann teoirimí ginearálta gaolta in iúl atá fíor do gach ball den tacar nithe atá luaite, ar nós: Tá bonnuillinneacha triantáin chomhchosaigh cothrom.
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Mathematics » Geometry » Coordinate Geometry A group is a set G on whose members a binary operation * may be carried out. The operation * when carried out on members of G has the following properties closure associativity existence of an identity element existence of an inverse.
Matamaitic » Céimseata » Céimseata Chomhordanáideach Is ionann grúpa agus tacar G ar féidir oibríocht dhénártha * a chur i ngníomh ar a bhaill. Tá na hairíonna seo a leanas ag an oibríocht * nuair a chuirtear i ngníomh ar bhaill G í: iamh comhthiomsaitheacht eiseadh baill céannachta eiseadh inbhéarta.
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Mathematics » Logic & Set Theory Two sets are said to be identical if and only if every element of each is an element of the other. When A and B are identical, we write A = B.
Matamaitic » Loighic & Tacartheoiric Deirtear go bhfuil dhá thacar comhionann más gá agus más leor gach ball de gach aon tacar a bheith ina bhall den tacar eile. Nuair atá A agus B comhionann, scríobhtar A = B.
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Mathematics » Logic & Set Theory An implication is a proposition formed from two propositions as an if...then statement.
Matamaitic » Loighic & Tacartheoiric Is ionann impleacht agus tairiscint a chumtar mar ráiteas má ... ansin ...
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Mathematics » Logic & Set Theory A set with an infinite number of elements e.g. the set of natural numbers or the set of real numbers.
Matamaitic » Loighic & Tacartheoiric Tacar a bhfuil líon éigríochta de bhaill ann e.g. tacar na n-uimhreacha aiceanta nó tacar na réaduimhreacha.
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Mathematics » Logic & Set Theory The intersection (or product) of the sets A and B is the set of elements belonging simultaneously to both A and B. [Similarly, for a greater (even infinite) number of sets.]
Matamaitic » Loighic & Tacartheoiric Is ionann idirmhír na dtacar A agus B agus tacar na mball a bhaineann go comhuaineach le A agus le B. [Is mar a chéile é do líon níos mó tacar (fiú do líon éigríochta).]
FÉACH FREISIN · SEE ALSO
# product of two sets · iolrach dhá thacar#
Let G be a group with elements a, b etc., and operation ○ also let G' be a group with elements a', b' etc., and operation ⊕. Then a 1 to 1 correspondence between G and G' defined by a ↔ a', b ↔ b', etc., is an isomorphism if and only if, for every a and b, a ○ b ↔ a' ⊕ b' The groups G and G' are called isomorphic.
Bíodh G ina ghrúpa le heilimintí a, b etc., agus le hoibríocht ○ freisin, bíodh G' ina ghrúpa le heilimintí a', b' etc., agus le hoibríocht ⊕. Ansin, iseamorfacht is ea comhfhreagras 1 le 1 idir G agus G' a shainítear le a ↔ a', b ↔ b', etc., más gá agus más leor, i gcás gach a agus b, go bhfuil a ○ b ↔ a' ⊕ b' Deirtear go bhfuil na grúpaí G agus G' iseamorfach.
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Mathematics » Logic & Set Theory At any stage of a proof we may replace a proposition or an open sentence by an equivalent one.
Matamaitic » Loighic & Tacartheoiric Ag staid ar bith de phróiseas cruthúnais, is féidir coibhéis tairisceana nó abairte oscailte a chur in ionad na tairisceana nó na habairte oscailte.
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Computers, Computer Science 1. The monadic Boolean operation whose result has the Boolean value opposite to that of the operand. 2. Synonymous with NOT operation.
Ríomhairí, Ríomheolaíocht 1. Oibríocht mhonadach Boole a bhfuil an luach Boole atá mar thoradh uirthi contrárthach le luach na hoibrinne. 2. Comhchiallach le hoibríocht NOT
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Mathematics » Logic & Set Theory The negation of a proposition is a new proposition which has the opposite truth value; i.e. if p is true, the negation of p is false and if p is false, the negation of p is true.
Matamaitic » Loighic & Tacartheoiric Is ionann séanadh tairisceana agus tairiscint nua a bhfuil luach fírinne contrártha aici; i. má tá p fíor, tá séanadh p bréagach agus má tá p bréagach, tá séanadh p fíor.
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Mathematics » Logic & Set Theory A set with at least one member.
Matamaitic » Loighic & Tacartheoiric Tacar ina bhfuil ball amháin ar a laghad.
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Mathematics » Logic & Set Theory An open propositional formula (or formula, for short) is an expression containing a finite number of variables p, q, r, etc., and a finite number of the logical operations: ∧ (and), ∨ (or), ¬ (not), → (implication), and ↔ (equivalence), which becomes a proposition when specific propositions are substituted for the variables.
Matamaitic » Loighic & Tacartheoiric Is slonn é foirmle thairisceanach oscailte (nó foirmle, mar a thugtar air go coitianta) ina bhfuil líon críochta athróg p, q, r, etc., agus líon críochta de na hoibríochtaí loighciúla: ∧ (agus), ∨ (nó), ¬ (ní), → (impleacht), agus ↔ (coibhéis), a ndéantar tairiscint de nuair a chuirtear tairiscintí sonracha in ionad na n-athróg.
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Mathematics » Logic & Set Theory An open sentence is a statement which contains a variable and which becomes a proposition when an element of the universal set is substituted for this variable. If the variable occurs more than once in the open sentence, the same element of the universal set must be substituted for it at each occurance.
Matamaitic » Loighic & Tacartheoiric Is ionann abairt oscailte agus ráiteas ina bhfuil athróg agus a ndéantar tairiscint de nuair a chuirtear ball den uilethacar in ionad na hathróige sin. Má tharlaíonn an athróg níos mó ná uair amháin san abairt oscailte, ní mór an ball céanna den uilethacar a chur ina hionad gach uair.
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Mathematics » Logic & Set Theory A term that appears to be immediately understandable and which is used without explaining its meaning.
Matamaitic » Loighic & Tacartheoiric Téarma a fheictear a bheith sothuigthe ar an toirt agus a úsáidtear gan é a mhíniú.
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Mathematics » Logic & Set Theory The intersection (or product) of the sets A and B is the set of elements belonging simultaneously to both A and B. [Similarly, for a greater (even infinite) number of sets.]
Matamaitic » Loighic & Tacartheoiric Is ionann idirmhír na dtacar A agus B agus tacar na mball a bhaineann go comhuaineach le A agus le B. [Is mar a chéile é do líon níos mó tacar (fiú do líon éigríochta).]
FÉACH FREISIN · SEE ALSO
# intersection of two sets · idirmhír dhá thacar#
Mathematics » Logic & Set Theory In this method, we assume that the given statement is true and then proceed to derive consequences from it. If we succeed in arriving at a consequence which contradicts a known theorem, we have shown that the given statement is false.
Matamaitic » Loighic & Tacartheoiric Ag úsáid an mhodha seo, glacaimid go bhfuil ráiteas áirithe fíor agus ansin cuirimid chun iarmhairtí a dhíorthú uaidh. Má éiríonn linn teacht ar iarmhairt a dhéanann teoirim aitheanta a bhréagnú, tá sé léirithe againn go bhfuil an ráiteas áirithe bréagach.
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Mathematics » Logic & Set Theory This method is used to disprove statements of the form: for all x in set X, the open sentence p(x) is true. To disprove such an assertion, we proceed to find a counter-example. In other words we look for one value of x for which the statement is false; and since the statement was supposed to be true for all values of x, this single counter example disproves the statement.
Matamaitic » Loighic & Tacartheoiric Úsáidtear an modh seo chun ráitis san fhoirm: do gach x sa tacar X, tá an abairt oscailte p(x) fíor a chruthú. Chun a leithéid de dhearbhú a chruthú, cuirimid chun frithshampla a aimsiú. Is é sin le rá, lorgaímid luach amháin de chuid x dá bhfuil an ráiteas bréagach; agus ó bhí an ráiteas in ainm is a bheith fíor do gach luach de chuid x, cruthaíonn an frithshampla amháin seo an ráiteas a bheith bréagach.
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Mathematics » Logic & Set Theory A proposition is a sentence to which one and only one of the terms true or false can be meaningfully applied.
Matamaitic » Loighic & Tacartheoiric Is ionann tairiscint agus abairt nach féidir ach ceann agus gan ach ceann de na téarmaí fíor nó bréagach a úsáid ina leith.
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GAcomhlánú fir coibhneasta dhá thacar▼
gu comhlánaithe choibhneasta dhá thacar, ai comhlánuithe coibhneasta dhá thacar
Mathematics » Logic & Set Theory The difference (or relative complement) of the sets A and B is the set of those elements of A which do not belong to B.
Matamaitic » Loighic & Tacartheoiric Is ionann an difríocht (nó an comhlánú coibhneasta) idir na tacair A agus B agus tacar na mball sin de A nach bhfuil i B.
FÉACH FREISIN · SEE ALSO
# difference of two sets · difríocht idir dhá thacar#
(finite grouping)
Mathematics » Logic & Set Theory A finite or infinite number of objects of any kind, of entities, or of concepts that have a given property or properties in common.
Matamaitic » Loighic & Tacartheoiric Líon críochta nó éigríochta de rudaí de chineál ar bith, de bheitheanna, nó de choincheapanna a bhfuil airí nó airíonna áirithe i gcoiteann acu.
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Mathematics » Logic & Set Theory A specific theorem states a fact about a particular mathematical object, such as: 7 is a prime number. 3.1416 is an approximate value for π.
Matamaitic » Loighic & Tacartheoiric Dearbhaíonn sainteoirim fíric faoi aonán matamaiticiúil ar leith, ar nós: Is uimhir phríomha é 7. Is neasluach do π é 3.1416.
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Mathematics » Logic & Set Theory A set A is a subset of the set B if and only if every element of A is an element of B
Matamaitic » Loighic & Tacartheoiric Is fo-thacar den tacar B é an tacar A más gá agus más leor gur ball de B é gach ball de A.
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Mathematics » Logic & Set Theory A formula is called a tautology if and only if it becomes a true proposition when any propositions whatsoever are substituted for its variables.
Matamaitic » Loighic & Tacartheoiric Tugtar athluaiteachas ar fhoirmle más gá agus más leor chun tairiscint fhíor a dhéanamh di go gcuirfí aon tairiscintí ar bith in ionad a cuid athróg.
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Mathematics » Logic & Set Theory The truth set of an open sentence is the set of all those elements of the universal set whose substitution in the open sentence results in true propositions.
Matamaitic » Loighic & Tacartheoiric Is ionann tacar fírinne abairte oscailte agus tacar na n-eilimintí sin go léir den uilethacar a dtarlaíonn tairiscintí fíora de bharr iad a chur in ionad na hathróige san abairt oscailte.
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Mathematics » Logic & Set Theory The truth value of a proposition may be either true or false but not both.
Matamaitic » Loighic & Tacartheoiric Féadann luach loighciúil tairisceana a bheith fíor nó bréagach ach ní fhéadann sé a bheith fíor agus bréagach.
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Mathematics » Logic & Set Theory The union (or sum) of the sets A and B is the set of those elements which belong to at least one of the sets. Similarly, for a greater (even infinite) number of sets.
Matamaitic » Loighic & Tacartheoiric Is ionann aontas (nó suim) na dtacar A agus B agus tacar na mball sin a bhaineann le ceann ar a laghad den dá thacar. Is mar a chéile é do líon níos mó de thacair, fiú do líon éigríochta.
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Mathematics » Logic & Set Theory When dealing with a given set of objects, there is always implied a large set or universal set to which all the objects belong. The universal set may vary from situation to situation, but is fixed for the duration of a particular discussion.
Matamaitic » Loighic & Tacartheoiric Nuair a bhítear ag déileáil le tacar ar leith de nithe, glactar leis i gcónaí gur ann do thacar mór nó do uilethacar lena mbaineann na nithe go léir. D'fhéadfadh uilethacair éagsúla a bheith i gceist i gcásanna éagsúla, ach is ar uilethacar seasta a bheifí ag trácht le linn aon díospóireachta ar leith.
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Mathematics » Logic & Set Theory Method of proof which proves the contrapositive of the statement, instead of the statement itself.
Matamaitic » Loighic & Tacartheoiric Modh cruthúnais a dhéanann frithdheimhneach an ráitis a chruthú, in ionad an ráiteas féin.