Which are more: rational or irrational numbers?

Now comes another amazing thing: there are multitudes of terminating decimal numbers and multitudes of non-terminating repeating decimals, but there are EVEN MORE non-terminating non-repeating decimals, or in other words irrational numbers. That is usually shown in college level mathematics courses. In mathematical terms we say that the rational numbers are a countable set whereas the irrational numbers are an uncountable set.

In other words, there are more irrational numbers than there are rational. Can you grasp that? It seems like something I accept as a proven fact but that is not tangible or easily illustrated in concrete terms — which is often the case with irrational numbers. They seem to elude us, yet are fascinating to think about.

The above is something I came across while browsing the internet. I started by looking at school district maps (Students sneaking into other districts to go to school.) and I wound up on a page about irrational numbers. Just going give my opinion on the title. I think of irrational numbers as the fog of war in a strategy game and rational numbers are what you can actively observe.