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.
2026-04-06 14:43:12.1775486592
Continuous variable defined over Rational numbers only?
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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 $x$).