12-07-2006, 05:00 AM | #21 |
Entmoot's Drunken Uncle
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Ah proofs... I miss proofs...
(And Proof! Hey CC! *nudge nudge wink wink*) My favorite was the Quadratic Formula. Ahem, if I may... IF a(x^2) + bx + c = 0 THEN x= -b (+or-) √[(b^2) - 4ac] ..............2a............... If you followed that, I love you. I love math. Unfortunatly, at the level I am at, the next class I would take would be specifically designed for those aspiring to be mathemeticians. I'm not mathemetician material. |
12-07-2006, 03:47 PM | #22 |
Entmoot Attorney-General,
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1200-year-old problem "easy"
A British mathematician claims to have solved the problem that occurs when you try to divide any number by zero. This is what he did: 0^0 = 0^(1-1) = 0^1 · 0^(-1) = (0/1)^1 · (0/1)^(-1) = 0/1 · 1/0 = 0/0 = a new number called "nullity" Very strange if you ask me. As I see it, the professor has just given a name to an undefined number. Easy indeed. Btw, does zero to the power of zero equal one? 0º=1 or not?
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12-07-2006, 04:58 PM | #23 |
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I think 0^0 should equal one...
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12-07-2006, 05:04 PM | #24 |
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That's what my calculator says too. But why?
Anything to the power of zero equals one. But at the same time, zero to the power of anything equals zero. So how the heck does one define 0^0?
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12-07-2006, 08:08 PM | #25 |
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To say that something is "too such and such a power" means it is multiplied by itself so many times. When you multiple zero by itself any number of times, you get zero. 0 x 0 = 0. 0 x 0 x 0 = 0. Et cetera. It stands to reason.
I don't know why something to the power of zero would equal one, however...it seems that, saying that you multiply it by itself zero times, you would either say it is the original itself, or it is zero; I lean more towards the former. Why is it said to equal one?
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12-07-2006, 11:03 PM | #26 | |
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Quote:
(x^a) * (x^b) can be written x^(a+b) If b = 0 we get (x^a) * (x^0) = x^(a+0) = x^a This means that x^0 = 1 The question is weather it still equals 1 for x = 0 edit: Or you can just enter any number into the nullity equation a couple of posts above. x for instance. You'll get that: x^0 = x/x = 1
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An unwritten post is a delightful universe of infinite possibilities. Set down one word, however, and it immediately becomes earthbound. Set down one sentence and it’s halfway to being just like every other bloody entry that’s ever been written. ☻ Last edited by Jonathan : 12-08-2006 at 02:43 AM. |
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12-08-2006, 01:02 AM | #27 | |
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Quote:
(0º) is undefined. At least under conventional mathematics. With calculus: lim(x^x) as (x goes to 0) (from the positive side) is equal to e^0 which is equal to 1 (I think this is why my TI-89 graphing calculator gives tells me that 0^0 = 1) My calculator says that 0^(-1) is undefined and 0^(1) = 0 yet 0^( 1 + [-1] ) = 1
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Sincerely, Anthony 'Many are my names in many countries,' he said. 'Mithrandir among the Elves, Tharkûn to the Drarves; Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not.' Faramir What nobler employment, or more valuable to the state, than that of the man who instructs the rising generation? Cicero (106BC-43BC) Last edited by mithrand1r : 12-08-2006 at 01:13 AM. |
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12-08-2006, 01:16 AM | #28 | |
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Quote:
Nullity * Nullity = ???? 3 + Nullity = ??? Nullity^Nullity = ??? What will a computer do with Nullity? I am just curious. (Interesting article.)
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Sincerely, Anthony 'Many are my names in many countries,' he said. 'Mithrandir among the Elves, Tharkûn to the Drarves; Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not.' Faramir What nobler employment, or more valuable to the state, than that of the man who instructs the rising generation? Cicero (106BC-43BC) |
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12-08-2006, 02:38 AM | #29 | |
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Quote:
From one thing to another, I've never come across any applications of the imaginary number i. I'm sure there must be some though. Does anyone know?
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12-08-2006, 02:51 AM | #30 | |
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people keep telling me to take a maths subject next year so i will have something practical at the end of my degree. well **** practicality if it means doing more maths
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12-08-2006, 02:54 AM | #31 |
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Math is fun. *creepy smile*
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12-08-2006, 11:16 AM | #32 | |||
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Quote:
Here are two qutoes from websites and what they say on the subject. http://www.newton.dep.anl.gov/newton...th/MATH033.HTM Quote:
Quote:
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Sincerely, Anthony 'Many are my names in many countries,' he said. 'Mithrandir among the Elves, Tharkûn to the Drarves; Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not.' Faramir What nobler employment, or more valuable to the state, than that of the man who instructs the rising generation? Cicero (106BC-43BC) |
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12-08-2006, 03:41 PM | #33 | |
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Quote:
Now that you say it, I remember that a friend told me too that complex numbers are used in electrical engineering. I had no idea about the quantum mechanics though. Anyone but me who thinks Euler's formula below is quite remarkable? e^(pi*i) + 1 = 0
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12-08-2006, 06:22 PM | #34 | |
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Quote:
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Crux fidelis, inter omnes arbor una nobilis. Nulla talem silva profert, fronde, flore, germine. Dulce lignum, dulce clavo, dulce pondus sustinens. 'With a melon?' - Eric Idle Last edited by Gwaimir Windgem : 12-08-2006 at 06:24 PM. |
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12-08-2006, 07:15 PM | #35 | |
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It has a little of everything.
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Sincerely, Anthony 'Many are my names in many countries,' he said. 'Mithrandir among the Elves, Tharkûn to the Drarves; Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not.' Faramir What nobler employment, or more valuable to the state, than that of the man who instructs the rising generation? Cicero (106BC-43BC) |
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12-09-2006, 06:36 AM | #36 | ||
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Quote:
Same thing about the nullity problem. But if there's any application of "nullity", it would be interesting to know. Quote:
Sine and cosine are also related since e^(X*i) = Cos(X) + i Sin(X) edit: I found a very educational site that deals with common mathematical fallacies and stuff. Zero Saga
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01-15-2008, 05:59 PM | #37 |
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09-25-2008, 03:25 PM | #38 |
Sapling
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Infinite Sets
So here's a cool thing mathematical fact that I'm surprised no one's brought up in this thread, and it's actually something even research mathematicians take into account today. Said imprecisely, infinity can be greater than infinity!
When you're determining the cardinality (size) of a set with a finite number of elements, you can just count the number of elements. Here's a simple example: Set B = {John, Mike, Tim, Dan, Steve} Set G = {Kim, Monica, Jane, Jessica} Set B has 5 elements, and Set G has 4 elements. Therefore, set B is larger. But, when you're dealing with infinite sets, you can't simply count the elements. The best you can do is try to compare elements between sets by forming a correspondence. We can actually apply this to the example above. Let's form a correspondence between Set B and G: John-Kim, Mike-Monica, Tim-Jane, Dan-Jessica... But wait! Set B has a leftover! It must be larger. This is very similar to how mathematicians compare infinite sets. So, let me get to the main result. The real numbers is an infinite set that is actually greater in cardinality than the natural numbers! The proof of this is called Cantor's Diagnolization Argument. This was actually really trippy stuff back in the day; not only did Cantor almost go insane thinking about it, he received threats from abroad. Last edited by JaeSon15 : 09-25-2008 at 03:30 PM. |
09-25-2008, 04:27 PM | #39 |
Elven Maiden
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Infinity is always weird... I was thinking earlier that there are infinite numbers between 1 and 2, but there are more numbers between 1 and 3. Something like that.
It's like in elementary where we would say "infinity plus 1" |
09-25-2008, 10:48 PM | #40 |
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I wonder if Achilles has passed the tortoise in the race yet...
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