[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 112: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 112: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 112: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 112: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/bbcode.php on line 112: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Notice: in file /includes/functions.php on line 4505: Cannot modify header information - headers already sent by (output started at /includes/functions.php:3706)
[phpBB Debug] PHP Notice: in file /includes/functions.php on line 4507: Cannot modify header information - headers already sent by (output started at /includes/functions.php:3706)
[phpBB Debug] PHP Notice: in file /includes/functions.php on line 4508: Cannot modify header information - headers already sent by (output started at /includes/functions.php:3706)
[phpBB Debug] PHP Notice: in file /includes/functions.php on line 4509: Cannot modify header information - headers already sent by (output started at /includes/functions.php:3706)
SMBC Comics Forum • View topic - [2011-May-18] Mathness of 1

[2011-May-18] Mathness of 1

Blame Quintushalls for this.

Moderators: NeatNit, Kimra

[2011-May-18] Mathness of 1

Postby Astrogirl » Wed May 18, 2011 11:13 am

http://www.smbc-comics.com/index.php?db=comics&id=2249

Is this last thing really 1? It surely somehow draws from e^(i*pi) being -1, but how?

I can't even read properly where is the base and where is the exponent. Either it says e^(i*pi/2) * i^i or it says e^(i*pi/2 * i^i).

i^i has infinitely many results: e^(-Pi/2 - 2*Pi*n) with n an integer. This is where I get lost.
crogression? !
User avatar
Astrogirl
so close, yet so far
 
Posts: 2114
Joined: Wed Aug 11, 2010 10:51 am

Re: Mathness of 1 [2011-May-18]

Postby zomgmouse » Wed May 18, 2011 11:21 am

(e^[pi*i]) +2 = 1
Better chocolate than choconever.
User avatar
zomgmouse
ss No More!
 
Posts: 862
Joined: Tue Sep 28, 2010 12:38 pm
Location: Melbourne, Australia

Re: Mathness of 1 [2011-May-18]

Postby Astrogirl » Wed May 18, 2011 11:28 am

Is this ... an answer to my question?
crogression? !
User avatar
Astrogirl
so close, yet so far
 
Posts: 2114
Joined: Wed Aug 11, 2010 10:51 am

Re: Mathness of 1 [2011-May-18]

Postby Felstaff » Wed May 18, 2011 11:39 am

HE MATHED AT YOU DIDN'T HE?!?
User avatar
Felstaff
XKCD spy
 
Posts: 787
Joined: Sun Jul 12, 2009 2:37 pm

Re: Mathness of 1 [2011-May-18]

Postby K^2 » Wed May 18, 2011 12:00 pm

User avatar
K^2
 
Posts: 13
Joined: Tue Mar 23, 2010 11:30 pm

Re: Mathness of 1 [2011-May-18]

Postby shining2k1 » Wed May 18, 2011 12:37 pm

Hey Astrogirl,

you smuggled an extra i into your first expression (force of habit, I guess). With e^(pi/2) *i^i instead of e^(i*pi/2) *i^i, the whole thing resolves to
e^(Pi/2-Pi/2 - 2*Pi*n)=e^(-2Pi*n)=1 for all whole numbers n
shining2k1
 

Re: Mathness of 1 [2011-May-18]

Postby Astrogirl » Wed May 18, 2011 1:36 pm

Ah, that suddenly makes a lot of sense. Indeed an extra i crept in on me.
crogression? !
User avatar
Astrogirl
so close, yet so far
 
Posts: 2114
Joined: Wed Aug 11, 2010 10:51 am

Re: Mathness of 1 [2011-May-18]

Postby K^2 » Wed May 18, 2011 1:39 pm

User avatar
K^2
 
Posts: 13
Joined: Tue Mar 23, 2010 11:30 pm

Re: Mathness of 1 [2011-May-18]

Postby orionsbelt » Wed May 18, 2011 1:49 pm

No one is going to point out that the caption says "Mathematicians are no longer allowed to sporting events"?
Sorry guys. I was a math major but I was also a writing minor. Awkward wording pops out to me. At me. Whatever you prefer.
orionsbelt
 

Re: Mathness of 1 [2011-May-18]

Postby JS » Wed May 18, 2011 2:09 pm

Oh, no, Zach; do you know what kind of can of worms you've opened? http://tinyurl.com/3tnvqh5
JS
 

Re: Mathness of 1 [2011-May-18]

Postby Kaharz » Wed May 18, 2011 3:27 pm

In the pop up he did note that that 0^0=1 depends on your definition. Always read the footnotes...
User avatar
Kaharz
This Intentionally Left Blank
 
Posts: 1572
Joined: Fri Feb 25, 2011 12:17 pm

Re: Mathness of 1 [2011-May-18]

Postby Mr. Pedantic » Wed May 18, 2011 4:56 pm

It is multi-valued.
e^(Pi/2) i^i = e^(Pi/2) e^(i ln i) = e^(Pi/2) e^(i (ln |i| + i arg(i))) = e^(Pi/2) e^(- Pi/2 - 2 n Pi) = e^(- 2 n Pi)
for any integer n. There is no 'i' term in the exponent, so this is not a single value. For n=0, we get 1 (and indeed, this would be the value associated with the principal branch of the complex logarithm), but it's just as reasonable to claim that this sign says "We're #e^(16 Pi)", (approximately 6.7 x 10^21)
Mr. Pedantic
 

Re: Mathness of 1 [2011-May-18]

Postby Oldrac the Chitinous » Wed May 18, 2011 6:01 pm

You know, if you just glance at the comic quickly, it looks kind of like the last sign says "We're Hentai."

Or maybe that's just me.
Police said they spent some time working out if they could charge the man with being armed with a weapon, as technically he was armed with part of a fish.
User avatar
Oldrac the Chitinous
Chicken O' the Sea
 
Posts: 3489
Joined: Fri Dec 12, 2008 11:41 pm
Location: The Perfect Stillness of the Deep

Re: Mathness of 1 [2011-May-18]

Postby Edminster » Wed May 18, 2011 6:16 pm

User avatar
Edminster
Tested positive for Space-AIDS
 
Posts: 8849
Joined: Fri Sep 09, 2005 9:53 pm
Location: Internet

Re: Mathness of 1 [2011-May-18]

Postby Tom Swift » Wed May 18, 2011 6:19 pm

Although it's a reasonable gripe that i^i has infinitely many possible values, I'm more concerned that the guy in the middle thinks 0^0 is 1. I think that maybe the mathematicians had a buddy from the physics department come along.

The value of 0^0 is "undefined". It's a classic trick question about double limits (limits of limits). It isn't 1: think about the limit of the limit of f(u,v) = u^v as both u and v go to 0. If you take the limit as u goes to 0 first (with v not 0) then that limit is 0. Do it the other way around and take the limit as v goes to 0 first and you get 1. So you can approach 0^0 two different ways and get two different answers for what it should be. If 0^0 really had a value, you couldn't get two different limits for it.
Tom Swift
 

Next

Return to Latest Comic Discussion 3: Revenge of the Son of Latest Comic Discussion 2

Who is online

Users browsing this forum: No registered users and 8 guests