DUH VORPY!!! DUH!!!
Your graphing calculator might just define 0^0 to be one. It’s probably more practical, since 0^x isn’t a very useful function.
Yeah, I think that’s the case; there appears to be a jump discontinuity at 0 for 0<sup>x</sup> anyway.
0/0=1 probably because any number/the same number=1.
0^0 should equal 0 because zero means nothing and nothing times nothing is still nothing.
Err, no. Try reading the posts in the thread before posting…
Some arguments in favor of defining 0^0 to be 1:
All this “0/0” talk reminds me of an anecdote my dad tells on occasion (he works at JPL). They had a calculator way back when that was mechanical rather than digital. You punched in some expression and it would noisily kerchunk along until it had an answer to spit at you. Unfortunately, it wasn’t very smart (insert adage about smart people in front of dumb terminals…), so the engineers, when bored, would go up to this calculator and divide something by zero. As it didn’t have any safeties against that kind of thing, apparently it would take whatever constant you gave it, subtract zero <i>kerchunk</i> and check to see if there was anything left.
Obviously, the thing would stubbornly continue kerchunking along, with no way to interrupt it and no end in sight, until someone came along to uplug the poor beast.
Probably not just 0<sup>0</sup>, but <i>a</i><sup>0</sup> as well. It’s not like your calculator can really take the limit anyway, due to series approximation and other stupid things that calculators can’t do.
I also seem to remember using <i>lim <sub>x->0</sub> 0<sup>x</sup></i> somewhere. Maybe it had something to do with using logarithms to determine if something converged or diverged.
I <i>really</i> need to read my calculus notes again…
Originally posted by <b>Setz</b>
Start with the factor: (a-a)(4-3)=0
Expand it into: a(4-3)-a(4-3)=0
This step <i>is</i> correct, despite what people have said. “FOIL” is a nice trick to expand expressions, but this partial expansion is also valid.
Since a=0: a(4-4)-a(3-3)=0
Take out common factors: 4a(1-1)-3a(1-1)=0
This is all proper algebra. Correct so far.
Divide each: 4a(1-1)/a(1-1)=3a(1-1)/a(1-1)=0
This is the error, of course. You divide by a(1-1), but a(1-1) = 0. Divide by zero error. Here’s a simplified version of your dilemma:
a = 0
a/a = 0/a
1 = 0
In everyday algebra, you just can’t divide by zero.
In Soviet Russia, zero divides by Setz!
This thread was posted, like, a week ago, by somebody else, right, and proved wrong at three or four different points, right? So why are we still talking about it?
Because people like posting in these gay-ass threads instead of my awesome hockey thread.
Or we all enjoy laughing at setz, and keeping it within everyone’s respective ‘radars’
lol 8 = 37
Here’s one for the math geniuses of the thread:
x=0
cos(x) = cos(0)
1/cos(x) + 1 = 1/cos(0) + 1
sin( 1/cos(x) + 1 )^2 = sin( 1/cos(0) + 1 )^2
1 - cos( 1/cos(x) + 1 )^2 = sin( 1/cos(0) + 1 )^2
( 1 - cos( 1/cos(x) + 1 )^2 ) / cos(x)^2 = tan( 1/cos(0) + 1 )^2
1 + ( sec(x)^2 - sec( 1/cos(x) + 1 )^2 ) = sec( 1/cos(0) + 1 )^2
cos( 1/cos(0) + 1 )^2( 1 + ( 1 / ( 1 - 1/csc(x)^2 ) - sec( 1/cos(x) + 1 )^2 ) ) = cos( 1/cos(0) + 1)^2( sec( 1/cos0) + 1 )^2
cos( 1/cos(0) + 1 )^2( 1 + ( 1 / ( 1 - 1/csc(x)^2 ) - sec( 1/cos(x) + 1 )^2 ) ) = 1
1 + ( 1 / ( 1 - 1/csc(x)^2 ) - sec( 1/cos(x) + 1 )^2 ) = sin( 1/cos(0) + 1 )^2
1 / ( 1 - 1/csc(x)^2 ) - sec( 1/cos(x) + 1 )^2 = -cos( 1/cos(0) + 1 )^2
Now, substituting 0 for x:
1 / ( 1 - 1/csc(0)^2 ) - sec( 1/cos(0) + 1 )^2 = -cos( 1/cos(0) + 1 )^2
1 / ( 1 - 1/csc(0)^2 ) = sec(2)^2 -cos(2)^2
1 - 1/csc(0)^2 = 1 / (sec(2)^2 -cos(2)^2)
1 / csc(0)^2 = 1 - 1 / (sec(2)^2 -cos(2)^2)
csc(0)^2 = 1 / ( 1 - 1 / (sec(2)^2 -cos(2)^2) )
sin(0)^2 = 1 / ( 1 / ( 1 - 1 / (sec(2)^2 -cos(2)^2) ) )
0 = 1 - 1 / (sec(2)^2 - cos(2)^2)
1 = 1 / (sec(2)^2 - cos(2)^2)
1 = sec(2)^2 - cos(2)^2
cos(2)^4 + cos(2)^2 - 1 = 0
cos(2)^4 + cos(2)^2 + .25 = 1.25
cos(2)^2 + .5 = sqrt(1.25)
cos(2) = sqrt( sqrt(1.25) - .5 )
The problem is that, really, cos(2) != sqrt( sqrt(1.25) - .5 ). cos(2) can be anything; it just depends on what system of measurement you use. So, what went wrong?
What’s the difference b/t Setz and GSG?
I don’t know either.
Well, neither of them necropost 5-year-old threads, for starters.
Well, I haven’t seen GSG show the least bit of interest in mathematics, for enders.
Come on dude. Five year necro?