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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>