Re: An uncountable countable set

Tony Orlow wrote:
Randy Poe wrote:
Tony Orlow wrote:
Randy Poe wrote:
Tony Orlow wrote:
Randy Poe wrote:
Tony Orlow wrote:
Virgil wrote:
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

.... much, leading nowhere.

Tony,

Would you care to answer me some questions? No tricks or anything, just
something about what we would call graphs in the x-y plane?

Here's a starter:

Consider a (notional, theoretical, mathematical, not physical) x-y
plane. That is, an area in which there is a point (0,0) in some
particular place, an x-axis, y-axis, and points are identified by
coordinates x and y, using (in normal maths) real values for these
coordinates. Consider (for convenience) that this plane is embedded in
a notional graphics application, with a "Fill" function. So if we draw
the circle x^2 + y^2 = 49 (centre origin, (constant! Zick, be quiet!)
radius 7), then click with the Fill function on the point (2,1), it
fills the circle, and no paint spills outside that radius 7.

Now suppose we have the graphs of x=2 and x=5. Vertical lines,
extending up and down without limit. Suppose we click with the Fill
function on the point (3, 4), what would you say happens? Obviously
paint fills the vertical strip of width 3. Would you say that any paint
was able to "spill" around the (nonexistent!) "top" of either of the
graphs, and somehow fill more of the plane than this strip, or would
you say we just get a (vertically) unbounded strip of blue? (Goddabe
blue!)

If you care to answer, I'd like to ask one or two more similar
questions. If you don't want to bother, please say, and I will save my
time.

Brian Chandler
http://imaginatorium.org

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