At least two circles tangent to y axis with nonempty intersection
Hi.
Here is a problem I've been trying to solve for some time now. Maybe you could help me.
We have two sets
is a set of those circles in the plane such that for any 
there exists a circle 
which intersects 
axis in )
.
is a set of those circles in the plane such that for any there exists a circle 
which is tangent to axis in .
Re: At least two circles tangent to y axis with nonempty intersection
Hey wilhelm.
Do you just have to show existence of such circles?
Re: At least two circles tangent to y axis with nonempty intersection
That's right. I think that maybe we could somehow identify each circle with a different rational number and this would mean that there is at most countably many disjoint circles in the plane but uncountably many points on x axis, so at least two must intersect. If this reasoning is right, it holds for both sets, doesn't it?
Re: At least two circles tangent to y axis with nonempty intersection
If this reasoning is right, it holds for both sets, doesn't it?
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