Counting Game(Stupid but addicting *maybe*)

[Error]

Hmh; I guess I'm not seeing it, then, but sqrt((-1)^2) does not normally equal -1 as your first equation states (the square root usually implies the principal/positive root), but that depends on which root you're looking for. If it's not the principal root 1 then the solutions would be ±1, and that makes your second equation perfectly valid as you'd get ±1=1 => 1=1, but that wouldn't imply that 2 = 0.

EDIT: So I guess the error is technically that the square root of (-1)^2 is neither 1 nor -1, but both?

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[Derkylos]

Root((-1)^2)=1, Root(-1^2)=i. Order of functions.

Also, n+1

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[Black Widow]

Root((-1)^2)=1, Root(-1^2)=i. Order of functions.

Also, n+1

actually your wrong: i = Root (-1), Root(-1^2) = Root ( -1 x -1) = Root ( 1 ) = +/-1

[Derkylos]

Read the syntax

Also, n+1

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[Corile]

It is a number since infinity = 1 / 0

What are you talking about.

<3serious5flood>
There seems to be a common belief that anything divided by zero equals infinity, which is not remotely the case. The result of this operation (x/0) is undefined, it's wrong and you don't do this. Because if it did, then 1/0 would equal to infinity, but so would 2/0, which would imply that 1=2. And I don't think that's how maths works.

There is a number, though, that is close to what you may want and that is the aleph null (א₀), which represents the cardinality (the number of elements) of the set of all natural integers (which is infinite, obviously), but it behaves a bit differently than your normal numbers (for example א₀ + 1 = א₀

You can also prove that x/0 is not equal to infinity just by looking at the graph of the function f(x)=1/x. As you approach the origin from the negative side, it will skyrocket up, towards positive infinity, but when you approach the origin from the positive side, it will go down, towards negative infinity.

That's all junior high school mathematics.
</3serious5flood>

also if you think that infinity - 1 must be a number

No, it's not a number, because that's kind of like saying potato - 1 is a number.

Stop spreading heresy, thanks.

I have degree in maths, my knowledge trumps yours

If you have a degree in maths and think that x/0 is infinity, you should give it up immediately and go back to high school.
Althernatively hit yourself in the head with a hammer.

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Reflections on the Revolution in Gallia
Custodi // High City of Heraklion // The Cult of Archangels
Log Filter // Post Creator // Manhattan

[Corile]

Hmh; I guess I'm not seeing it, then, but sqrt((-1)^2) does not normally equal -1 as your first equation states (the square root usually implies the principal/positive root), but that depends on which root you're looking for. If it's not the principal root 1 then the solutions would be ±1, and that makes your second equation perfectly valid as you'd get ±1=1 => 1=1, but that wouldn't imply that 2 = 0.

EDIT: So I guess the error is technically that the square root of (-1)^2 is neither 1 nor -1, but both?

I'm almost sure that it's 1, because a square root squared doesn't equal the original number but rather the absolute value of the original number.
I might be wrong though as imaginary numbers are ways away of my area of expertise.

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Reflections on the Revolution in Gallia
Custodi // High City of Heraklion // The Cult of Archangels
Log Filter // Post Creator // Manhattan

[Thyrzul]

Edit: I think I misunderstood that, so here's a quick note regarding the case of 1/x: the function will never cross the y-axis and will thus not "flip" signs as it approaches infinity, as 1/0 is not defined as stated earlier.

It's rather a consensus than an observation that the graph of the 1/x function never crosses any of the axes. But theoretically it could, in the infinity (not when just approaching it), where then it flips signs and continues going back towards zero. Imagine linear functions actually being 3D circles with infinite radius. For them you'd need two points where values flip signs, one is zero, the other can be infinity.

(More mindfech: x/0=inf. and x/inf.=0 could be easily possible and show how similar they are, even tho the current mathematical consensus is that x/0=undefined and only lim(y->0)x/y=inf., same going for the x/inf. values.)

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[Bulldog.]

Seems like Disco now has its own University.

With all this debate on the theory of Infinity, I have lost track of the count xD

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[Yber]

Root((-1)^2)=1, Root(-1^2)=i. Order of functions.
Also, n+1

actually your wrong: i = Root (-1), Root(-1^2) = Root ( -1 x -1) = Root ( 1 ) = +/-1

lol.
Root[-1]= +-i
But nevermind that.
You got it right Error. It's a problem about definitions.
1= (+-1)^2:
a) (1)^2= Root[(1)^2]= 1.
b) (-1)^2= |Root[(-1)^2]|= 1.
Because (-1)^2 is always a positive number. Positive numbers always return positive roots (in the case of real numbers) and thus absolute value is applied to the result.

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inb4 Sirius gets renamed to XTF.

[Bulldog.]

All I can say to your calculations is derp

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