Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let X be a random variable taking the value 0.2 with probability 0.2, 0.4 with probability 0.4 and 0.8 with probability 0.2 and 1.0 with probability 0.2.

Using Infinitary logic I can ask the probability:

$$P(X = P(X = P(X = \ldots)))$$

How is is this value computed?

share|improve this question
I don't see how you can express anything close to anything looking like the thing you wrote with infinitary logic. Maybe you just want to study the set $\{x \in [0;1] / P(X=x) = x\}$ ? –  mercio Nov 22 '11 at 13:00
If you think this expression belongs to the framework of infinitary logic, you should explain why. Otherwise one could get the feeling that, to you, infinitary logic is a shorthand for everything seemingly paradoxical and with $\cdots$ in it. –  Did Nov 27 '11 at 11:21

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.