Re: Rational Numbers/Irrational Numbers

On Jan 26, 11:36 pm, "David T. Ashley" <d...@xxxxxxxx> wrote:
"Leo" <newsdon...@xxxxxxxxxxx> wrote in messagenews:1169780763.086460.114690@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Which set has more numbers, the set of rational numbers or the set of
irrational numbers?
Well, the set of irrational numbers has at least twice as many elements as
the set of rational numbers.

Think about the following functions:

f(x) = PI + x
g(x) = PI + PI + x

Every rational number x can be paired with at least two irrationals.

So, I'm going to go with "irrational" as being bigger.

Right answer. Wrong reason. The rationals are countable. The
irrationals are uncountable. The rationals have Lebesgue measure zero.
The irrationals in [0,1] have Lebesgue measure 1.

.

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