4 ms·
for the Reals, it is only hypothetical, the domain has a total order. \inf and $\inf + 1$ comes to mind but I don't think it really counts
by kevindamm 3y ago
for the Reals, it is only hypothetical, the domain has a total order.
\inf and $\inf + 1$ comes to mind but I don't think it really counts
- thaumasiotes 3y ago> \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".
- kaba0 3y agoI 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`.