Originally posted by Leonhard
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Tower of powers
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Originally posted by lao tzu View PostIt's a natural error. Everything else in PEMDAS evaluates "ties" left to right, except exponents, which evaluate right to left."[Mathematics] is the revealer of every genuine truth, for it knows every hidden secret, and bears the key to every subtlety of letters; whoever, then, has the effrontery to pursue physics while neglecting mathematics should know from the start he will never make his entry through the portals of wisdom."
--Thomas Bradwardine, De Continuo (c. 1325)
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Originally posted by Boxing Pythagoras View PostInteresting. I've never really thought about it before, since Commutativity very often makes the question moot. However, 1/2/2=x would seem a good example of this discrepancy. Are there any others?
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Originally posted by lao tzu View PostIs .999... = 1?
Jim
PS Another simple way of validating .999...=1 is:
x = .9999....
10x = 9.9999......
9.9999.... - .99999.... = 9
thus (10x-x)=9 -> 9x=9 -> x=1Last edited by oxmixmudd; 01-30-2015, 08:57 AM.My brethren, do not hold your faith in our glorious Lord Jesus Christ with an attitude of personal favoritism. James 2:1
If anyone thinks himself to be religious, and yet does not bridle his tongue but deceives his own heart, this man’s religion is worthless James 1:26
This you know, my beloved brethren. But everyone must be quick to hear, slow to speak and slow to anger; James 1:19
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Np - It's been that kind of day
JimMy brethren, do not hold your faith in our glorious Lord Jesus Christ with an attitude of personal favoritism. James 2:1
If anyone thinks himself to be religious, and yet does not bridle his tongue but deceives his own heart, this man’s religion is worthless James 1:26
This you know, my beloved brethren. But everyone must be quick to hear, slow to speak and slow to anger; James 1:19
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Originally posted by klaus54 View Postsqrt(2)^sqrt(2)^sqrt(2) = 2
You are confusing this Power Tower with a very different case, which is CodeCogsEqn (5).gif
These are two entirely different expressions."[Mathematics] is the revealer of every genuine truth, for it knows every hidden secret, and bears the key to every subtlety of letters; whoever, then, has the effrontery to pursue physics while neglecting mathematics should know from the start he will never make his entry through the portals of wisdom."
--Thomas Bradwardine, De Continuo (c. 1325)
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Originally posted by Boxing Pythagoras View PostThis is incorrect. [ATTACH=CONFIG]3817[/ATTACH]
You are confusing this Power Tower with a very different case, which is [ATTACH=CONFIG]3818[/ATTACH]
These are two entirely different expressions.
Simple use [img ][/img ], and use the handy URL encoding that the CodeCog's Equation Editor uses. Its located down under the editor. This loads faster, and uses less memory on the tweb server, as you offload the fetch to the CodeCog server which seems to be optimized to handle cases like this.
Here as example I wrote that equation below as [img ]http://latex.codecogs.com/png.latex?%5Cdpi%7B200%7D%20f%28z%29%20%3D%20z%5E% 7Bz%5E%7Bz%5E%7B...%7D%7D%7D[/img ]
Also... please... please please please, stop writing the tower power like
Ugly ugly ugly! You might as well just write it in ascii. This implies that the tower power is merely, z to the power of z which has been raised to the power z. Instead write it like this
(latex code: f(z)=z^{z^{z^{...}}})
So that people can see that this process goes on forever.Last edited by Leonhard; 02-04-2015, 03:16 AM.
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Originally posted by klaus54 View Postsqrt(2)^sqrt(2)^sqrt(2) = 2
The tower grows from there.
Confused...
K54
f(z) = z^z^z
But
f(z) = z^z^z^z^z^z^z^...
Secondly I assume of course the ordinary order right right to left, but to make it clearer this is what it looks like with parenthesees.
f(z) = z^(z^(z^(z^(z^(z^(z^(z^(...))))))))
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Originally posted by Leonhard View PostFirst of all (and I'll write it in ascii this time), it's not,
f(z) = z^z^z
But
f(z) = z^z^z^z^z^z^z^...
Secondly I assume of course the ordinary order right right to left, but to make it clearer this is what it looks like with parenthesees.
f(z) = z^(z^(z^(z^(z^(z^(z^(z^(...))))))))
How does one start at the "end" of an infinite sequence in order to work right to left??
K54
P.S. E.g., sqrt(2)^((sqrt(2))^(sqrt(2)) is approximately 1.76
This demonstrates where I was wrong.
P.P.S. And I had forgotten the right to left convention for evaluating exponents. Sorry...
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Originally posted by klaus54 View Post...
How does one start at the "end" of an infinite sequence in order to work right to left?? (ETA: Or top to bottom when there's no "top"?)
...
Thanks!
K54
P.S. ETA: I get it now... (took me a hour or so of cogitation.) Look at a sequence of the values of n towers as n increases without bound.Last edited by klaus54; 02-04-2015, 10:18 PM.
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