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| AgentDrake |
 Posted: Wed Dec 12, 2007 4:29 pm |
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Joined: 01 Apr 2007
Posts: 667
Location: Halfway between eccentric and insane...
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3i is defined. It has a specific value. Granted, you can’t get anything in the physical world to achieve that value, but it has a fixed, defined value.
∞ does not have a specified value. No matter what value you pick, ∞ is always infinitely larger.
3i is a number. "imaginary" number, but a number nonetheless.
∞ is not a number. It is the concept of an unlimited number set. |
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| NBarden |
| Posted: Wed Dec 12, 2007 4:41 pm |
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Joined: 28 Dec 2006
Posts: 5468
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Wrong. According to my math professor and math textbook, 3i is undefined. Why else do you need to ensure the domain of a function doesn’t result in an imaginary number? Because its undefined.
If you define 3i, then you have to define infinity. That simple. |
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| AgentDrake |
| Posted: Wed Dec 12, 2007 4:46 pm |
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Joined: 01 Apr 2007
Posts: 667
Location: Halfway between eccentric and insane...
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3i is defined, but not in terms of Real Numbers.
It is defined as the value 3√-1 (√-1 = i)
∞ is "defined" as the concept of an infinite number set.
It is not a "defined" value. |
| Never kid about politicians. The more bizarre the joke, the more likely it is to come true. |
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| NBarden |
| Posted: Wed Dec 12, 2007 4:49 pm |
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Joined: 28 Dec 2006
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It is defined as a conceptual number.
The reality is that by the same rule that division by 0 is undefined, 0^infinity is also undefined. A lot of operations by 0 are undefined, 0^X only applies to real numbers, of which infinity is not. It is a number, but not real.
The second one is quite simple. Each number has a positive and negative root. for f(X) = SQRT(X) (DOMAIN: X > 0), any number will result in a positive or negative. Proof.
f(4) = SQRT(4)
f(4) = 2 or f(4) = -2
CHECK: 2^2 = 4 and (-2)^2 = 4.
Thus, SQRT(4)=±2
Applying that to number 2...
±SQRT 25 = ±SQRT [(-1)(-1)(25)] (what you do to one side, you can do to the other)
±SQRT 25 = ±SQRT (-1) * SQRT (-1) * SQRT (25) (splitting apart square roots is legal if number is in multiplicative form)
±5 = ±i * i * 5 (SQRT of -1 = i)
±5 = ±i^2 * 5 (i * i = I squared)
±5 = ±5 (i^2 = -1)
±1=±1 (divide both sides by 5)
Make more sense? |
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Add the popcorn smiley to your sig, help it achieve world domination.
What if the hokey pokey really IS what its all about?
As I lay in bed staring at the stars last night, I thought to myself, "where the heck is the ceiling?"
Spotlight on....Sense of Obligation. |
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| AgentDrake |
| Posted: Wed Dec 12, 2007 5:00 pm |
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Joined: 01 Apr 2007
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Location: Halfway between eccentric and insane...
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Not sure, but I think we were arguing two contradictory ways of saying the same thing. Don’t have time to look through it again at the moment, but I’ll check again later. |
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| Elessar's Socks |
| Posted: Wed Dec 12, 2007 5:05 pm |
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Joined: 29 Jul 2007
Posts: 349
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Infinity is not a number. It’s a common misconception that results in more bizarre "proofs" that you can shake a radical at.
When we say 1/∞ = 0, what we really mean is
lim{x->∞} 1/x = 0.
In other words, the limit of 1/x, as x grows arbitrarily large, approaches 0. ∞ is a form of shorthand, but it is not a number.
NBarden wrote: If X to the ∞ (infinity) power = ∞, and 0 to the Y power = 0 (DOMAIN: X=All Real Numbers, Y=All real Numbers), then does 0 to the ∞ power simultaneously equal 0 and infinity, in which case, are zero and infinity equal?
I believe this is how it works out:
lim{x->∞} a^x = ∞, where a > 1
lim{x->∞} a^x = 1, where a = 1
lim{x->∞} a^x = 0, where 0 ≤ a < 1
Zero and infinity are not equal.
Quote: 25 = 25 (fundamental duh)
25 = (-1)(-1)(25) (negative of a negative is a positive)
SQRT 25 = SQRT [(-1)(-1)(25)] (what you do to one side, you can do to the other)
SQRT 25 = SQRT (-1) * SQRT (-1) * SQRT (25) (splitting apart square roots is legal if number is in multiplicative form)
You should know the answer to this already, if you were able to answer the complex number paradox a while ago. The square root of -1 (I say that instead of i to emphasize the square root) is not a real square root, so manipulating the radicals in this case leads to a paradox.
Edit - Oops, was a little careless. lim{x->∞} 1^x should be 1, but 1^∞, by itself, is an indeterminate form. |
| Last edited by Elessar's Socks on Wed Dec 12, 2007 11:36 pm; edited 1 time in total |
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| NBarden |
| Posted: Wed Dec 12, 2007 5:18 pm |
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Joined: 28 Dec 2006
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I knew the flaws in it, but its still fun to use rules of math, ignoring exceptions (like sqrt both sides of the equation makes ± both sides of the equation, exception to what you do to one side you do to the other). Infinity isn’t a number? But a limit, and a way of expressing something that IS defined. So infinity IS defined. Which is what I was saying.
I know my math well enough to know that none of what I said was true, but I thought it’d be fun to try to stump everyone. |
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Add the popcorn smiley to your sig, help it achieve world domination.
What if the hokey pokey really IS what its all about?
As I lay in bed staring at the stars last night, I thought to myself, "where the heck is the ceiling?"
Spotlight on....Sense of Obligation. |
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| gil-estel |
| Posted: Wed Dec 12, 2007 5:32 pm |
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Joined: 25 Apr 2007
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Location: Groningen, the Netherlands
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| NBarden |
| Posted: Wed Dec 12, 2007 5:38 pm |
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| gil-estel |
| Posted: Wed Dec 12, 2007 6:30 pm |
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Joined: 25 Apr 2007
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Location: Groningen, the Netherlands
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| The only thing I know, is that I know nothing...once said by a man whome some consider to be the wisest of all....do you know the name of this man? And maybe what he meant by saying this? |
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