Re: Exponents and notation

*To*: mathgroup at smc.vnet.net*Subject*: [mg29885] Re: [mg29876] Exponents and notation*From*: "Michael" <michael at science.edu>*Date*: Tue, 17 Jul 2001 01:00:31 -0400 (EDT)*References*: <200107160428.AAA13406@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

> From: "Ludwig Deruyck" <dr01202 at pophost.mediring.be> To: mathgroup at smc.vnet.net > To: <mathgroup at smc.vnet.net> > Sent: Sunday, July 15, 2001 11:28 PM > Subject: [mg29885] [mg29876] Exponents and notation > > Solving '2^3^4^5' with a HP48G+ (Algebraic mode) gives as a result: > 1.1529150461E18 > This is the solution of ((2^3)^4)^5. But is this correct? > > Using: > 5 > 4 > 3 > 2 in equation writer gives an overflow. I believe this is the correct > way of reading '2^3^4^5' > 2^3^4^5 should be the same thing as 2^(3^(4^5)). To prove this, try: In[1]:= 4^5 Out[1]= 1024 In[2]:= 3^4^5 == 3^1024 Out[2]= True In[2]:= 3^4^5 Out[2]= 3733918487410200435329597541848665882254097767837340077506369317220790406172 65\ 2512299936889388039772204687650654314751581087270545921608585813513369828091 87\ 3141917485942625809388070199519564042855718180410466812887974029255176680123 40\ 6172983965747316191523867230462351259348960585905882846547935405059362023765 47\ 8074427305821445270589887562514528177934133521419207446230275187291854328623 75\ 7370639854853194764169262638199728870069070138992565242971985276987492741962 76\ 811060702333710356481 So I would not try to raise two to this power and expect Mathematica to come back with a result any time soon. > In Mathematica '2^3^4^5' is evaluated as a general overflow, so this is read > in the correct way. > Hmm, this is the first I've seen the 'General::"ovfl": "Overflow occurred in computation."' message. If I try a different calculation, say 8^8^8, I don't get an overflow, but instead Mathematica just happily tries to find the results (but I'm not holding my breath). > Is the HP wrong ? > > Well it would seem to be grouping the operators differently, but there may be a good reason for this? > L.DERUYCK > mailto:dr01202 at pophost.mediring.be > Michael

**References**:**Exponents and notation***From:*"Ludwig Deruyck" <dr01202@pophost.mediring.be>