The point of using 3^^^3 is to avoid the need to assign precise values, which I agree seems impossible to do with any confidence. Once you accept the premise that A is less than B (with both being finite and nonzero), you need to accept that there exists some number k where kA is greater than B. The objections have been that A=0, B is infinite, or the operation kA is not only nonlinear, but bounded. The first may be valid for specks but misses the point—just change it to “mild hangnail” or “banged funnybone.” I cannot take the second seriously. The third is tempting when disguised as something like “you cannot compare a banged funnybone with torture” but becomes less appealing when you ask “can it really cause (virtually) zero harm to bang a trillion funnybones just because you’ve already banged 10^100?”
It was the need for a “magical line” as in Unknown’s example that convinced me. I’m truly curious why it fails to convince others. I admit I may be missing something but it seems very simple at its core.
Joseph,
The point of using 3^^^3 is to avoid the need to assign precise values, which I agree seems impossible to do with any confidence. Once you accept the premise that A is less than B (with both being finite and nonzero), you need to accept that there exists some number k where kA is greater than B. The objections have been that A=0, B is infinite, or the operation kA is not only nonlinear, but bounded. The first may be valid for specks but misses the point—just change it to “mild hangnail” or “banged funnybone.” I cannot take the second seriously. The third is tempting when disguised as something like “you cannot compare a banged funnybone with torture” but becomes less appealing when you ask “can it really cause (virtually) zero harm to bang a trillion funnybones just because you’ve already banged 10^100?”
It was the need for a “magical line” as in Unknown’s example that convinced me. I’m truly curious why it fails to convince others. I admit I may be missing something but it seems very simple at its core.