Forum:Double Approximations

Suggestion: In pages of numbers, use double approximations (i.e. with a lower bound and an upper bound) instead of single approximations (i.e. with either a lower bound or an upper bound, but not both).

For instance, gugold is approximated to \(100\uparrow^{100}101\) in up-arrow notation, which is a lower bound. But it also has an upper bound \(101\uparrow^{100}101\). And the double approximation of gugold is \(100\uparrow^{100}101<\text{gugold}<101\uparrow^{100}101\).

Currently we use single approximation, in which we need to choose one of the two ends (lower or upper bound). However, it's not easy to determine the closer end of the two, because they're "googological". The "middle" of 3 and 7625597484987 can be 3812798742495 (in linear scale), 4782969 (in logarithmic scale) or 27 (in anti-tetrational scale). Then what's the "middle" of \(100\uparrow^{100}101\) and \(101\uparrow^{100}101\)?

And using double approximations is an option to avoid these kind of problems. &#123;hyp/^,cos&#125; (talk) 09:36, June 18, 2017 (UTC)