Question

In: Advanced Math

Show that a set is convex if and only if its intersection with any line is...

Show that a set is convex if and only if its intersection with any line is convex. Show that a set is affine if and only if its intersection with any line is affine.

Solutions

Expert Solution

Colby Messinger answered 2 years ago
Next > < Previous

Related Solutions

Find a set of parametric equations for the tangent line to the curve of intersection of...
Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces at the given point. (Enter your answers as a comma-separated list of equations.) z = x2 + y2,    z = 16 − y,    (4, −1, 17)
Find a set of parametric equations for the tangent line to the curve of intersection of...
Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces at the given point. (Enter your answers as a comma-separated list of equations.) z = sqrt(x2 + y2) , 9x − 3y + 5z = 40, (3, 4, 5)
let S in Rn be convex set. show that u point in S is extreme point...
let S in Rn be convex set. show that u point in S is extreme point of S if and only if u is not convex combination of other points of S.
Prove the principle of transmissibility. Show that any force can be moved along its line of...
Prove the principle of transmissibility. Show that any force can be moved along its line of action resulting in the same external motion of the object.
Show that a point x is an accumulation point of a set E if and only...
Show that a point x is an accumulation point of a set E if and only if for every ε > 0 there are at least two points belonging to the set E ∩ (x − ε, x + ε).
Use only the operators discussed in class (select, project, Cartesian product, join, union, intersection, set difference...
Use only the operators discussed in class (select, project, Cartesian product, join, union, intersection, set difference and renaming). Type your answers. The following database schema is given: ATHLETE(name,age,height,weight,country) RACE(id,location,date,time-start,distance) COMPETES(aname,rid,time,position) where ATHLETE has information about runners (their name, age, height, weight, and nationality); RACE has information about races (id, location, date when it’s held, time it starts, and distance ran); and COMPETES keeps track of which runners run on with race, the time it took them to complete the race,...
Use only the operators discussed in class (select, project, Cartesian product, join, union, intersection, set difference...
Use only the operators discussed in class (select, project, Cartesian product, join, union, intersection, set difference and renaming). Type your answers. Consider the following database schema: INGREDIENT(ingredient-id,name,price-ounce) RECIPE(recipe-id,name,country,time) USES(rid,iid,quantity) where INGREDIENT lists ingredient information (id, name, and the price per ounce); RECIPE lists recipe information (id, name, country of origin, and time it takes to cook it); and USES tells us which ingredients (and how much of each) a recipe uses. The primary key of each table is underlined; rid...
Let X be a non-empty set and P(X) its power set. Then (P(x), symetric difference, intersection)...
Let X be a non-empty set and P(X) its power set. Then (P(x), symetric difference, intersection) is a ring. Find a non-trivial ideal of P(X).
Show that a set S has infinite elements if and only if it has a subset...
Show that a set S has infinite elements if and only if it has a subset U such that (1) U does not equal to S and (2) U and S have the same cardinality.
Show that any portfolio on the Capital Market Line (CML) with a positive weight in the...
Show that any portfolio on the Capital Market Line (CML) with a positive weight in the market portfolio is perfectly correlated with the market portfolio. Interpret this result.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT