Equation object makes replace function not work

Stop talking about functions from calculators and computers, they are merely an aid, not a solution.
In maths I can honestly say that Arcsin is NOT a particularly common function, but if I am correct the closer x gets to 0, from the equation Arcsin(x), the closer the result gets to +- infinity, simple differentiation, well not that simple...Your calc gives you 0 coz its a ****ing calculator! Not a deep blue super computer, which itself would give you 0, since the correct answer is +- infinity and computers can't deal with this. I am going to have a guess and say that you're less than 20 years old. Younger generation rely far too much on calcs and computers to give them an answer :( *sigh*

Sqrt(x) is a computer function, it cannot return a + and -, so the default is +!!!
Computers and calcs can't deal with i, that's the problem, i is a complex number!!! Actually that's not tue, but Sqrt(-1) will give you an error...what level have you studied maths too?! I am intregued coz you ain't have spouted a load of bollox :D

25^(1/2) does = 5 and "only" 5 for < 11yr olds! But that it to only keep it simple and not confuse them at such an early stange!

Have you ever dealt with complex numbers? Can you prove the exist? Have you done 3D integration using complex numbers??? Thought not...well I have so I think I have a btter grash of what is going on. Oh...and a calc/comp never even got used!!! All done on paper *sigh*

:D

Woka

http://www.angelfire.com/or2/mathtutor/pie-eyed.html

Quote:

---

Take square roots; by definition the square root of a number is that which, multiplied by itself, gives the original number as the result, or
(n0.5)2 = n
Assuming that the product of like signs is always positive has the result that all positive numbers have two different square roots (one negative, one positive), while no negative number can have a square root.

---

Interesting.

If I was answering a question, for example, what is the square root of 25?, I would give two answers.

I am not totally sure of the definition of the "square root of a number", but going on the reasoning above, the answer would clearly be ±5.

5² = 5 * 5 = 25
-5² = -5 * -5 = 25 (Negative * Negative = Positive - Basic Maths :p)

At least that's roughly my understanding.

s.

Exactally. Basic Maths...

However,

-5^2 = -25
(-5)^2 = 25 ;)

Sorry, am being pedantic now, sorry...Hahahahaha

Woka

You knew what I meant :p

s.

Well, you're both right.

Mr. Panda-looking-icon is correct to say that positive numbers have 2 square roots
(hoggin all the negative's stuff! those dirty F$)%#*&...)

Bugz is right to say that a function only returns one value. But functions are only one part of math...

and BTW: When i put a high-degree polynomial into my calculator (it has nice SOLVE function*) it actually returns ALL the possible answers. (X = 1 or X = 3)

*: A function that returns more then 1 value! Must be a string :)

Or an array :D

Woka

PS OY! It's a ****ing badger not a pander! *SoB*

OK, there is a simple explanation to all this.
And thats the key, SIMPLIFICATION

sqrt(x) = + sqtr(x) cos mathematicians can't be bothered writing the + sign in before it.

its like in the quadratic formula, the +/- bit. that qualifies which root u r talking about.

1+2 = +1+2, but the former is easier.
in the same way:
sqrt(x) - sqrt(x) = +sqrt(x) - [+sqrt(x)] = 0
AND:
sqrt(x) - sqrt(x) = +sqrt(x) + [-sqrt(x)] = 0

So yeah, every real >0 has two roots:
+sqrt(x) and -sqrt(x)
but due to mathematician liking to simplify stuff (hence sigma notation, etc...) +sqrt(x) often becomes sqrt(x).

(BTW, functions by definition return 1 value, otherwise they are not a function. However, inverse functions -like x^(1/2) AND arcsin- are ofte relations instead)

Sorry Mr. Panda...err..Badger-looking-icon ;)

One thing I thought about in the first week of summer break was:

4-2 not= 2-4 but +4-2 = -2+4 so....
4/2 not= 2/4 but *4/2 = /2*4

I wonder why we never have a divion as the first symbol... (assumed to be a one in front, /2 = .5)