3 ms·
It reminded me of the 'paradox' that 1 + 0.5 + 0.25 + 0.125... is finite and not even very large. You could have an infinite universe with infinitely many stars
by gurkendoktor 14y ago
It reminded me of the 'paradox' that 1 + 0.5 + 0.25 + 0.125... is finite and not even very large. You could have an infinite universe with infinitely many stars and still end up with a certain percentage of the sky being dark.
Or maybe I'm mathematically wrong, but the above summation has broken any intuition for me that "the sum of infinitely many things must certainly surpass everything" :(
- thaumasiotes 14y agoThat sum is even easier to process as finite if you represent it in binary: 1 + 0.1 + 0.01 + 0.001 + 0.0001 +... clearly, after any number of terms have gone by, you're still not at two (though of course, once they all have, you are).
- gurkendoktor 14y agoOh, that's a nice explanation. I like to think that I am not adding something, just always going half the way to 2.0. Still, when this was introduced to me in school, I remember my head hurting a little. :)