Solution Set

In mathematics, a solution set for a collection of polynomials \{f_i\} over some ring R is defined to be the set \{x\in R:\forall i\in I, f_i(x)=0\}.

Examples

1. The solution set of f(x):=x over the real numbers is the set {0}. 2. For any non-zero polynomial f over the complex numbers in one variable, the solution set is made up of finitely many points. However, for a complex polynomial in more than one variable the solution set has no isolated points.

Remarks

In algebraic geometry solution sets are used to define the Zariski topology. See affine varieties.

 

<< PreviousWord BrowserNext >>
eamonn ceannt
boursin cheese
vaktoth heavy fighter
list of people involved with babylon 5
fiend club
florida a&m university
simon frith
spessard holland
kemi sami
bernard henry philip petre, 14th baron petre
holland & knight
groupe d'intervention de la gendarmerie nationale
hobey baker award
miami tornadoes of 2003
goaltender
wickwar
battle of majuba hill
particle velocity level
green lake
initium
vedic mathematics (book)
heaven can wait
south atlantic tropical cyclone
unholy passion ep
severn beach
excalibur heavy fighter
november coming fire
penalty (ice hockey)
acidophilus
experience wwii
subsidiary
sexual inhibition
muskoka river
morton, south gloucestershire
endicott
ishiro honda
paula vogel
sherbrooke, nova scotia
david auburn
over, south gloucestershire
tony fletcher
weakly harmonic
wnnx (fm)
almondsbury