I have a set containing all of the odd integers in the integer set. It is denoted by $O=\{2n+1\mid n\in \mathbb{Z}\}$. I want to write an equation that equals the standard deviation of the set. If I already know that $$\sigma=\sqrt{\frac{\sum(x_i-\mu)^2}{N}}$$ is the formula for standard deviation, where $\sigma$ represents the standard deviation, $N$ represents the length of the set, $x_i$ represents each value of the set, $\mu$ represents the population mean of the set, and the set I have is indefinitely long, then how can I write the equation?
2026-03-27 10:13:02.1774606382
What is the equation for the standard deviation of the set of all odd integers?
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