| Date Posted: Fri Dec/16/11 at 9:19am |
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so for the equation
lim √x
x→0
if approaching from the positive, than it would naturally be 0, both when approaching from both sides, I have been told it doesn't exist, however doing the math out:
√-4 = i2
√-1 = i1
√-0 = i0
the negitive side clearly approaches 0, just on the imaginary plane.
Could somebody explain why it doesn't exist?
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| Date Posted: Fri Dec/16/11 at 9:24am |
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Turbine |
Posts: 10194
Joined: 26-Oct-09 |
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I'm not in Calculus or anything, but I'd think that it can't approach from the imaginary side, because that would lead to an imaginary answer, which isn't very useful. Also, how are you going to represent imaginary numbers in a graph?
[Edited by Turbine on 16/Dec/11 at 9:25AM] |
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| Date Posted: Fri Dec/16/11 at 9:25am |
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Because it's an imaginary 0. If it was clear that the sequence was approaching -0, then you could say that the limit was 0 (from the negative side).
Multiplying any number by "i" results in a number that is imaginary (does not exist). |
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| Date Posted: Fri Dec/16/11 at 9:25am |
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Although it leads to an imaginary answer, imaginary 0 is the same as 0.
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| Date Posted: Fri Dec/16/11 at 9:26am |
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Imaginary 1 is not the same as 1. Imaginary 1 = i, whereas 1 = 1... |
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| Date Posted: Fri Dec/16/11 at 9:29am |
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Turbine |
Posts: 10194
Joined: 26-Oct-09 |
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So,  -1 * 0 != 0? Why is that?
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| Date Posted: Fri Dec/16/11 at 9:30am |
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I finished Calc yesterday. Pal's answer is pretty spot on.
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| Date Posted: Fri Dec/16/11 at 9:33am |
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Turbine |
Posts: 10194
Joined: 26-Oct-09 |
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I'm only in Geometry right now. Next year, I'm taking Pre-Calc.
Why don't imaginary numbers mix with real numbers at all? Do they follow the same rules?
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| Date Posted: Fri Dec/16/11 at 9:42am |
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Exactly, Turbine. Math is not exact. Just like there is no answer to the problem:
44 divided by 0... |
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| Date Posted: Fri Dec/16/11 at 9:45am |
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Of course I1 isn't equal to 1, but -1 isn't equal to 1, but -0 is equal to 0, and so i0 is equal to 0.
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| Date Posted: Fri Dec/16/11 at 9:45am |
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Turbine |
Posts: 10194
Joined: 26-Oct-09 |
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Better question: 42 / 0
Also, if there isn't reasoning for these rules, then how were they created? Also, you'd better be joking about that math isn't exact! I love math, because it allows me to learn universal truths!
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| Date Posted: Fri Dec/16/11 at 9:51am |
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Math is NOT exact. Don't be fooled by the Zealots.
there is no -0. If you are looking at the number line, on one side is negative numbers, on the other side is positive numbers. the number 0 is the line that separates them, neither negative, nor positive. When someone refers to -0 (usually in limits) they mean it approaches 0 from the negative side.
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| Date Posted: Fri Dec/16/11 at 9:54am |
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and if you look on the imaginary plane, when the imaginary axis reaches zero its at the same point as real zero.
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| Date Posted: Fri Dec/16/11 at 9:56am |
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Turbine |
Posts: 10194
Joined: 26-Oct-09 |
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What does an imaginary plane even look like???
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| Date Posted: Fri Dec/16/11 at 9:57am |
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| Date Posted: Fri Dec/16/11 at 9:59am |
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Turbine |
Posts: 10194
Joined: 26-Oct-09 |
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Why, that explains it! Unicorns are the source of imaginary numbers! |
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| Date Posted: Fri Dec/16/11 at 9:59am |
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Best potrayed by a two axis grid, the Y axis is instead the Imaginary axis, and X axis is instead the Real axis, this axis however is naturally not part of the X or Y (or Z or W) axis, it is its own axis.
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| Date Posted: Fri Dec/16/11 at 10:01am |
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Sounds like Math has an Axis to grind... |
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| Date Posted: Fri Dec/16/11 at 10:25am |
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Turbine |
Posts: 10194
Joined: 26-Oct-09 |
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Facehoof
That's how you graph complex numbers. How do you graph simply imaginary numbers? Is there a special way, or is it just a number line?
[Edited by Turbine on 16/Dec/11 at 10:32AM] |
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| Date Posted: Fri Dec/16/11 at 10:59am |
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Just a number line, perpendicular to the real number line (intersects at zero)
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| Date Posted: Fri Dec/16/11 at 11:28am |
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Turbine |
Posts: 10194
Joined: 26-Oct-09 |
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Pal, join us and the thread will be entirely full of ponies! |
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| Date Posted: Fri Dec/16/11 at 1:17pm |
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I guess because The Two-Gun Kid is riding a horse that counts |
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