> \inf and $\inf + 1$ comes to mind but I don't think it really counts
That just depends on the numeric structure you're working with. In the extended reals, +inf is equal to +inf + 1.
In a structure with more infinite values than that, it would generally be less. But they wouldn't be incomparable; nothing says "comparable values" quite like the pair "x" and "x + 1".
I guess it depends on the exact definitions, but reals usually doesn’t include the infinities. At my uni we introduced infinities precisely as an extension of the reals with two values defined by `lim`.
\inf and $\inf + 1$ comes to mind but I don't think it really counts