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Let $x(t)$ be a solution of some first order ODE, which is continuous over $t$. In this case, is the continuous $x(t)$ defined only over Rational numbers? what is the reason behind this? Please clarify me if I am wrong.

Ron
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1 Answers1

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Your question may need further clarification. However, I guess you are wondering about the following fact. If $x:\Bbb R\to\Bbb R$ is continuous and we know values of $x$ at rational points, then we know $x$ everywhere (just by taking limits thanks to the continuity of $x$).

SBF
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  • I think you have explained me about a stopping time proof in http://math.stackexchange.com/questions/351984/stopping-time-proof In that proof, can you kindly explain me the sentence "intersection over rational numbers only since X has continuous trajectories. Thanks to you.

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     – Ron May 17 '13 at 15:10