@davide405 wrote:
Hello Mike, welcome to the BoingBoing forums Image may be NSFW.
Clik here to view.I think by "hit with a dart" she means: randomly select one of the infinite number of points on the real number line.
Put another way, let's make it the real number haystack. We'll let every one of the irrational numbers be represented by a strand of hay. Now in that infinite pile of hay, we're going to have an infinite number of needles, which will each stand for a rational number.
The reason the chances of drawing one of the needles from the haystack is 0% is because of the different size (cardinality) of the infinities involved. There are a bunch of needles, make no mistake, but for every needle, there is an infinite number of pieces of hay. So, the chance that the thing you draw from the haystack is a needle is 1/infinity.
We don't have a good way to understand what that means until we approach it with the concept of limits. We say "limit of f(x)= 1/x as x approaches positive infinity" and it turns out, that's 0.
Actually, it's that every rational number, when expressed as a "decimal" is an infinite sequence of repeating digits, no matter what the base. It so happens that some rational numbers tail out with an infinite sequence of repeating zeros, which we customarily don't bother to write.
It's about a wash as to whether it's tidier to write 1/3 or 0.3... But it's definitely easier to write 1/7 than it is to write 0.142857... In most cases the representation of a rational number as a ratio is more compact.
