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Title: so math and stuff
Date Posted: Fri Dec/16/11 at 9:19am

lin sivvi
Posts: 1608
Joined: 14-Jan-10

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?
Date Posted: Fri Dec/16/11 at 9:24am

Turbine
Posts: 10194
Joined: 26-Oct-09

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]
Date Posted: Fri Dec/16/11 at 9:25am

Pal-of-Lim-Dul
Posts: 1148
Joined: 24-May-10

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).
Date Posted: Fri Dec/16/11 at 9:25am

lin sivvi
Posts: 1608
Joined: 14-Jan-10

Although it leads to an imaginary answer, imaginary 0 is the same as 0.
Date Posted: Fri Dec/16/11 at 9:26am

Pal-of-Lim-Dul
Posts: 1148
Joined: 24-May-10

Imaginary 1 is not the same as 1. Imaginary 1 = i, whereas 1 = 1...
Date Posted: Fri Dec/16/11 at 9:29am

Turbine
Posts: 10194
Joined: 26-Oct-09

So, scriptstyle sqrt{,,}-1 * 0 != 0? Why is that?
Date Posted: Fri Dec/16/11 at 9:30am

Twogunkid
Posts: 2610
Joined: 22-Jan-10

I finished Calc yesterday. Pal's answer is pretty spot on.
Date Posted: Fri Dec/16/11 at 9:33am

Turbine
Posts: 10194
Joined: 26-Oct-09

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?
Date Posted: Fri Dec/16/11 at 9:42am

Pal-of-Lim-Dul
Posts: 1148
Joined: 24-May-10

Exactly, Turbine. Math is not exact. Just like there is no answer to the problem:

44 divided by 0...
Date Posted: Fri Dec/16/11 at 9:45am

lin sivvi
Posts: 1608
Joined: 14-Jan-10

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.
Date Posted: Fri Dec/16/11 at 9:45am

Turbine
Posts: 10194
Joined: 26-Oct-09

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! 
Date Posted: Fri Dec/16/11 at 9:51am

Pal-of-Lim-Dul
Posts: 1148
Joined: 24-May-10

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.
Date Posted: Fri Dec/16/11 at 9:54am

lin sivvi
Posts: 1608
Joined: 14-Jan-10

and if you look on the imaginary plane, when the imaginary axis reaches zero its at the same point as real zero.
Date Posted: Fri Dec/16/11 at 9:56am

Turbine
Posts: 10194
Joined: 26-Oct-09

What does an imaginary plane even look like???
Date Posted: Fri Dec/16/11 at 9:57am

Pal-of-Lim-Dul
Posts: 1148
Joined: 24-May-10

A pony.
Date Posted: Fri Dec/16/11 at 9:59am

Turbine
Posts: 10194
Joined: 26-Oct-09

Why, that explains it! Unicorns are the source of imaginary numbers!
Date Posted: Fri Dec/16/11 at 9:59am

lin sivvi
Posts: 1608
Joined: 14-Jan-10

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.
Date Posted: Fri Dec/16/11 at 10:01am

Pal-of-Lim-Dul
Posts: 1148
Joined: 24-May-10

Sounds like Math has an Axis to grind...
Date Posted: Fri Dec/16/11 at 10:25am

Turbine
Posts: 10194
Joined: 26-Oct-09

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]
Date Posted: Fri Dec/16/11 at 10:59am

lin sivvi
Posts: 1608
Joined: 14-Jan-10

Just a number line, perpendicular to the real number line (intersects at zero)
Date Posted: Fri Dec/16/11 at 11:28am

Turbine
Posts: 10194
Joined: 26-Oct-09

Pal, join us and the thread will be entirely full of ponies!
Date Posted: Fri Dec/16/11 at 1:17pm

Twogunkid
Posts: 2610
Joined: 22-Jan-10

I guess because The Two-Gun Kid is riding a horse that counts



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