User:Vel!/pu/weakExE

ExE uses "strong hyperoperators" - hyperoperators that go a{n}b = a{n-1}(a{n-1}(...(a{n-1}(a{n-1}a))...)), but what if we had ExE with weak hyperoperators - hyperoperators that go a{n}b = ((...((a{n-1}a){n-1}a)...){n-1}a){n-1}a?
 * E100(#^#)^#100 = E100#^##100 (gridgahlah)
 * E100((#^#)^#)^#100 = E100#^###100 (kubikahlah)
 * E100(((#^#)^#)^#)^#100 = E100#^####100 (quarticahlah)
 * E100#vv#100 = E100#^#^#99 ~ godgathor
 * E100#vv#100#2 = E100#^#^#((E#^#^#99)-1) ~ grand godgathor
 * E100#vv#100#100 ~ E100#^#^#100#100
 * E100#vv#100#vv#100 ~ gotrigathor
 * E100#vv#*#100 ~ E100#^#^#*#100
 * E100#vv#*#vv#100 ~ deutero-godgathor
 * E100(#vv#)^#100 ~ hecato-godgathor
 * E100((#vv#)^#)^#100 = E100(#vv#)^## ~ godgridgathor
 * E100(#vv#)^#^#100 ~ godgathordeus
 * E100(#vv#)^(#^#*#^#)100 ~ godgathortruce

To make things more compact, let's shorten E100@100 to E@


 * E(#vv#)^(#^#)^# ~ gralgathor
 * E(#vv#)^((#^#)^#)^# ~ thraelgathor
 * E(#vv#)^(#vv#) ~ godtothol
 * E(#vv#)^(#vv#)^(#vv#) ~ godtertol
 * E(#vv#)^(#vv#)^(#vv#)^(#vv#) ~ godhathor

Wait a minute...


 * E((#vv#)^(#vv#))^(#vv#) ~ godtotholdeus
 * E(((#vv#)^(#vv#))^(#vv#))^(#vv#) ~ godtotholtruce
 * E(#vv#)vv# ~ graltothol
 * E((#vv#)vv#)^((#vv#)vv#) ~ gralhathor
 * E100((#vv#)vv#)vv#3 ~ gralhathordeus
 * E((#vv#)vv#)vv# ~ godhathorfact
 * E(((#vv#)vv#)vv#)vv# ~ something in the godheptol range
 * E#vvv# ~ E100#^^#102 = tethrathothi-bitoth

We've reached the tethrathoth range, but we had to go through two operators instead of one. And it will be much harder to get even halfway to Pentacthulhum (Strong operators are much more stronger than weak operators on hyperions then they are on numbers, if you get what I mean). That's why ExE uses strong hyperoperators.