Translation examples
verb
verb
Jos (varas) on tehnyt varkauden yöllä, (ja) jos (varkauden uhri) tappaa hänet, olkoon (varas) surmattu oikeuden mukaan.
If thieves by night, they will destroy till they have enough.
Olkoon θ kulma, jonka y-akselilla olevan pisteen (0,b) kautta kulkeva suora muodostaa y-akselin kanssa.
For example, any line passing through the point (0, 1) on the y-axis and having infinitesimal slope is parallel to the x-axis.
verb
Jos ƒ on konveksi, niin kaikilla x , y , z ∈ I {\displaystyle x,y,z\in I} on voimassa f ( x ) + f ( y ) + f ( z ) 3 + f ( x + y + z 3 ) ≥ 2 3 . {\displaystyle {\begin{aligned}&{}\qquad {\frac {f(x)+f(y)+f(z)}{3}}+f\left({\frac {x+y+z}{3}}\right)\\&\geq {\frac {2}{3}}\left.\end{aligned}}} Epäyhtälö voidaan yleistää n pisteelle: Olkoon ƒ jatkuva kuvaus joukosta I ⊆ R {\displaystyle I\subseteq \mathbb {R} } joukkoon R {\displaystyle \mathbb {R} } .
If f is convex, then for any three points x, y, z in I, f ( x ) + f ( y ) + f ( z ) 3 + f ( x + y + z 3 ) ≥ 2 3 . {\displaystyle {\frac {f(x)+f(y)+f(z)}{3}}+f\left({\frac {x+y+z}{3}}\right)\geq {\frac {2}{3}}\left.} If a function f is continuous, then it is convex if and only if the above inequality holds for all x, y, z from I {\displaystyle I} .
verb
Tähän intuitioon perustuu nk. jatkuvuuden ε δ {\textstyle \varepsilon \delta } -määritelmä (kreikk. ''epsilon'' ja ''delta''), joka on seuraava: Olkoon I ⊂ R {\textstyle I\subset \mathbb {R} } väli, a ∈ I {\textstyle a\in I} ja f : I → R {\textstyle f:I\to \mathbb {R} } .
A Lie algebra extension h ↪ i t ↠ s g , {\displaystyle {\mathfrak {h}}\;{\overset {i}{\hookrightarrow }}\;{\mathfrak {t}}\;{\overset {s}{\twoheadrightarrow }}\;{\mathfrak {g}},} is trivial if there is a subspace i such that t = i ⊕ ker s and i is an ideal in t.
verb
Islam opettaa itse, että profeetta Muhammed (Jonka olkoon rauha ja Allahin siunaukset) oli profeettojen sinetti, jonka jälkeen ei tule muita profeettoja.
Islam proclaims that its prophet Muhammad was the "seal of the prophets" and no further prophets would come after him.
verb
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