It is not known whether $\pi+e, \pi-e, \frac{\pi}{e}, etc$ are irrational, it has also been shown that at least one of the numbers $\zeta(5), \zeta(7), \zeta(9), \zeta(11)$ is irrational. From my point of view, it looks "obvious" that all these numbers are irrational however proving them is a different story. Do you know of any numbers that seem irrational/transcendental at first glance but actually aren't? (except $e^{i\pi}$)
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