5 ms·
It is not equal to zero. It is infinitesimal. There is a difference.
by levythe 8y ago
It is not equal to zero. It is infinitesimal. There is a difference.
- Sharlin 8y agoInfinitesimals don't exist in standard analysis. There exist no positive numbers smaller than all positive real numbers. The probability of picking any given real number from [0, 1) is exactly zero, there's no other number it could be. Rigorously, the measure of any countable subset of real numbers is zero.
- deepsun 8y agoHonestly, I don't really "like" real numbers, exactly because they are defined as classes of equivalence of converging sequences of neighborhoods. But I'm pretty sure even in rational numbers probability would be exactly zero, because that's how probability there is defined (as a limit of a sequence, and limit is zero).