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3h
comment Is there a name for dividing a set into pieces, some of which may be empty?
The system of abstract convexity I am interested in, usually it is called a closure system, has as axioms: The sets $\varnothing$ and $X$ are convex. If $\mathcal{C}$ is a collection of convex sets then so is $\cap \mathcal{C}$. The vector space example is an instance of the situation I am interested in.
4h
comment Is The *Mona Lisa* in the complement of the Mandelbrot set.
Thank you. That seems like it will work. There will be a certain amount of tediousness to fill in the details.
4h
accepted Is The *Mona Lisa* in the complement of the Mandelbrot set.
4h
awarded  Nice Question
8h
asked Is there a name for dividing a set into pieces, some of which may be empty?
9h
comment Is The *Mona Lisa* in the complement of the Mandelbrot set.
Your answer is an idea for a proof. I think that something like that will work. Unfortunately thinking something will work is not the same as proving it works. The hard part is describing the judicious positioning.
Apr
20
awarded  Yearling
Apr
19
comment Is The *Mona Lisa* in the complement of the Mandelbrot set.
If you look at the first picture at this link: artyfactory.com/art_appreciation/portraits/chuck_close.html you will see something like the type of picture I mean. The difference is that Chuck Close has doo-dads in the squares. I would use solid colors.
Apr
10
comment Classifying Types of Paradoxes: Liar's Paradox, Et Alia
@Memming That's what I wanted. Thanks.
Apr
10
revised Classifying Types of Paradoxes: Liar's Paradox, Et Alia
Changed the reference.
Jan
15
answered How to justify “two-dimensional” induction
Dec
10
awarded  Caucus
Oct
30
comment discuss convexity of the following set?
mfl's suggestion to plot the region is a very good idea.
Oct
9
reviewed Looks OK Conditional Integral of Square of Brownian Motion?
Oct
6
answered Subset Relation: Is the subset relation a partial order?
Oct
6
answered Prove that if X is a subset of Y then X intersect Z is a subset of Y intersect Z for all sets X, Y, Z.
Sep
24
awarded  Autobiographer
Sep
8
comment The family of finite unions of half-open intervals forms a ring of sets
It the nth term and the mth term do not intersect then you have written the empty set in a complicated way. You can delete all these different versions of writing the empty set.
Sep
8
comment Why is the set of functions from the naturals to the rationals a subset of $\mathcal P(\mathbb N \times \mathbb Q)$?
What is your definition of a function? What is your definition of an element of $\mathcal{P}(\mathbb{N} \times \mathbb{Q})$?
Sep
8
comment The family of finite unions of half-open intervals forms a ring of sets
Use the distributive property for $A \cap B$. See what you get.