C2 · 50 words
Pure mathematics in Spanish
Set, map, structure, theorem — the language mathematics is written in.
One structure in this list has a different metaphor in each language, and the Spanish one is the odd match for us. El cuerpo algebraico is what English calls a field: the structure where you may divide by anything except zero. Spanish — like German with Körper — calls it a body. And Spanish does have el campo, which is our field in every other sense: the field of wheat, el campo magnético, el campo semántico. So the two words cross exactly once, and only in algebra. El cuerpo keeps its ordinary jobs alongside: the human body, and a corps of people — el cuerpo de bomberos, the fire brigade.
The words
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Phrase (37)
el subconjunto propiothe part of a set that does not use the whole of it upPhraseC2
El subconjunto propio no agota al conjunto.A proper subset does not exhaust the set.
el conjunto vacíothe set with no members at allPhraseC2
El conjunto vacío es subconjunto de todos.The empty set is a subset of every set.
la unión de conjuntosthe set holding everything from both, counted oncePhraseC2
La unión de conjuntos no cuenta dos veces.The union does not count anything twice.
el producto cartesianothe set of all ordered pairs from two setsPhraseC2
El producto cartesiano forma pares ordenados.The Cartesian product forms ordered pairs.
el cardinal transfinitothe size that lets two infinite sets be comparedPhraseC2
El cardinal transfinito compara conjuntos infinitos.The transfinite cardinal compares infinite sets.
el conjunto numerablethe infinite set that can still be put in a queuePhraseC2
El conjunto numerable se puede poner en fila.A countable set can be put in a row.
la relación de equivalenciathe relation that sorts a set into classesPhraseC2
La relación de equivalencia divide en clases.An equivalence relation divides into classes.
la clase de equivalenciathe class gathering what the relation cannot tell apartPhraseC2
La clase de equivalencia reúne lo indistinguible.An equivalence class gathers what cannot be told apart.
el orden parcialthe ordering that leaves some pairs uncomparedPhraseC2
El orden parcial deja elementos sin comparar.A partial order leaves elements uncompared.
la aplicación inyectivathe map that never sends two things to the same placePhraseC2
La aplicación inyectiva no repite imágenes.An injective map does not repeat images.
la aplicación sobreyectivathe map that reaches every point of the targetPhraseC2
La aplicación sobreyectiva alcanza todo el codominio.A surjective map reaches the whole codomain.
el grupo algebraicothe structure with one operation, a neutral element and inversesPhraseC2
El grupo algebraico necesita elemento neutro e inverso.A group needs a neutral element and inverses.
el cuerpo algebraicothe structure where anything but zero may be divided byPhraseC2
El cuerpo algebraico permite dividir salvo por cero.A field allows division except by zero.
el espacio vectorialthe structure where vectors are added and scaledPhraseC2
El espacio vectorial se describe por una base.A vector space is described by a basis.
la base del espaciothe smallest set of vectors that spans the whole spacePhraseC2
La base del espacio no es única.The basis of a space is not unique.
la dimensión del espaciothe number of vectors in any such set, which never variesPhraseC2
La dimensión del espacio sí es única.The dimension of a space is unique.
la independencia linealthe property that none of them can be built from the othersPhraseC2
La independencia lineal impide expresar uno por los otros.Linear independence stops one being expressed by the others.
el núcleo de una aplicaciónwhat a map sends to zero, and so a measure of what it losesPhraseC2
El núcleo de una aplicación mide cuánto se pierde.The kernel of a map measures how much is lost.
el valor propio de una matrizthe number a matrix leaves unchanged along one directionPhraseC2
El valor propio de una matriz resuelve la ecuación característica.The eigenvalue of a matrix solves the characteristic equation.
el límite de una sucesiónthe value a sequence draws towards, if it draws anywherePhraseC2
El límite de una sucesión no siempre existe.The limit of a sequence does not always exist.
la convergencia uniformethe kind of convergence that carries continuity with itPhraseC2
La convergencia uniforme conserva la continuidad.Uniform convergence preserves continuity.
la serie divergentethe sum that never settles on a valuePhraseC2
La serie divergente puede crecer muy despacio.A divergent series can grow very slowly.
la continuidad de una funciónthe property of having no jumps, defined with epsilon and deltaPhraseC2
La continuidad de una función se define con épsilon y delta.Continuity is defined with epsilon and delta.
la integral definidathe area under a curve between two points, a numberPhraseC2
La integral definida es un número, no una función.The definite integral is a number, not a function.
el teorema fundamental del cálculothe result that ties the two operations of calculus togetherPhraseC2
El teorema fundamental del cálculo une las dos operaciones.The fundamental theorem of calculus joins the two operations.
el espacio métricothe space that needs nothing but a notion of distancePhraseC2
El espacio métrico solo necesita una noción de distancia.A metric space needs only a notion of distance.
el conjunto abiertothe set that does not contain its own edgePhraseC2
El conjunto abierto no contiene su frontera.An open set does not contain its boundary.
el invariante topológicothe property that no deformation can changePhraseC2
El invariante topológico distingue lo que no se puede deformar.A topological invariant tells apart what cannot be deformed.
el número primothe number divisible by nothing but one and itselfPhraseC2
El número primo no tiene divisores propios.A prime number has no proper divisors.
la factorización únicathe theorem that the prime factors are always the same onesPhraseC2
La factorización única es un teorema, no una obviedad.Unique factorisation is a theorem, not an obvious truth.
la congruencia modularthe arithmetic that works with remaindersPhraseC2
La congruencia modular trabaja con restos.Modular congruence works with remainders.
el lema auxiliarthe helper result proved on the way to the real onePhraseC2
El lema auxiliar prepara el terreno.The auxiliary lemma prepares the ground.
la hipótesis del teoremathe condition without which the theorem does not holdPhraseC2
La hipótesis del teorema no se puede quitar sin más.The hypothesis of the theorem cannot simply be dropped.
la demostración constructivathe proof that shows how to get the thingPhraseC2
La demostración constructiva enseña cómo obtenerlo.A constructive proof shows how to obtain it.
la demostración de existenciathe proof that the thing exists without saying wherePhraseC2
La demostración de existencia no dice dónde está.An existence proof does not say where it is.
la generalidad del resultadothe reach of a result, measured by how little it assumesPhraseC2
La generalidad del resultado se mide por lo que supone.The generality of a result is measured by what it assumes.
la elegancia de la pruebathe quality of a proof that makes it seen rather than followedPhraseC2
La elegancia de la prueba no es un adorno para el que la lee.The elegance of a proof is no ornament for the reader.
Noun (m) (6)
el conjuntothe collection fixed by which things belong to itNoun (m)C2
El conjunto se define por sus elementos.A set is defined by its elements.
el anillothe structure with a second operation addedNoun (m)C2
El anillo añade una segunda operación.A ring adds a second operation.
el determinantethe number whose vanishing says a matrix has no inverseNoun (m)C2
El determinante nulo señala una matriz sin inversa.A vanishing determinant marks a matrix with no inverse.
el homeomorfismothe map that deforms one shape into another and backNoun (m)C2
El homeomorfismo identifica formas que se pueden deformar una en otra.A homeomorphism identifies shapes that deform into one another.
el teoremathe result that was wantedNoun (m)C2
El teorema es el resultado que se quería.The theorem is the result that was wanted.
el corolariothe result that falls out almost without extra workNoun (m)C2
El corolario sale casi sin trabajo adicional.The corollary comes out almost without further work.
Noun (f) (7)
la intersecciónthe set holding only what both haveNoun (f)C2
La intersección puede quedar vacía.The intersection may come out empty.
la diagonalizaciónthe argument that showed some infinities are biggerNoun (f)C2
La diagonalización demostró que hay infinitos mayores.Diagonalisation proved that there are bigger infinities.
la biyecciónthe map that does both, and lets one count by pairing offNoun (f)C2
La biyección permite contar comparando.A bijection allows counting by comparison.
la derivadathe rate of change, which is a limit and not a formulaNoun (f)C2
La derivada es un límite, no una fórmula.The derivative is a limit, not a formula.
la topologíathe study of what survives being stretchedNoun (f)C2
La topología estudia lo que resiste una deformación.Topology studies what withstands a deformation.
la compacidadthe property that lets a convergent subsequence be pulled outNoun (f)C2
La compacidad permite extraer subsucesiones convergentes.Compactness allows convergent subsequences to be extracted.
la conjeturathe statement believed and not yet provedNoun (f)C2
La conjetura resiste mientras nadie la demuestre.A conjecture holds as long as nobody proves it.
This list belongs to Nature and natural sciences — 31 lists and 1550 words that can also be practised as a whole.
Practise this list
From these 50 words, as many per round as you like — up to all of them: first what is due today, then new ones. First you choose, then you fill the gap, then you write it yourself. Mistakes come back again shortly.