One of my math teachers discussed stochastic ("random") variables today. In an example, he discussed the probability of picking a random number n, such that [itex]n\inℝ[/itex], in the interval [0,10]. He proceeded to say that the probability of picking the integer 4 ([itex]n = 4[/itex]) is 0, supporting his claim with the statement that [itex]\frac{1}{\infty} = 0[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

Now, I'm well aware that I am being extremely picky with this, especially since this is a high school class. However, if one wanted to be pedantic, one might say the following:

- [itex]P(4\in\textbf{Z}) = \frac{1}{|N|}[/itex], where Z denotes the set of integers and |N| denotes the cardinality of the set N, where N is defined as the set of all real numbers in the interval [0,10].
- The value of [itex]P(4\in\textbf{Z})[/itex] is infinitesimal, but not exactly zero.
- Though the cardinality of the set N (defined in #1) is infinite, it is not truly correct to use the lemniscate (∞) to denote the quantity.

Are these all correct statements? If so, which one(s) are incorrect?

Thank you in advance for your verifications/corrections. :tongue2:

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# Regarding continuous stochastic variables and probability

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