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Mr Example.

Name: Anonymous 2007-08-30 13:43 ID:eUFPtE+p

I enjoyed those two Monsieur Ejemplé threads so I thought I'd pose a maths question of my own, in fact I'll do two on countability. They're not that hard, but I think they're more enjoyable than calculus

1. Let f : R -> R be monotonic.
Is  the set { x | f is discontinous at x} countable?
where x is in R.


2. A function f : N -> N is increaing if f(n)>= f(n+1)   (if it's bigger than OR equal to) and a decreasing function is similarly defined.

is the set {f | f is increasing} countable?
is the set {f | f is decreasing} countable?

Name: Anonymous 2007-08-31 16:06 ID:y2gYpBvg

>>5
Do you mean that the outlines of no two touch, or that the area enclosed by no two overlaps?

I believe the first can generate an uncountably infinite collection, the second only a countably infinite one.

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