DarkGizmo, that hotel money example is pretty flawed, since you thought the flaw was that 25+27=/=30, but the point was that 27-2=25, or 30-3-2=25
Infinity annoys me... 2xInfinity=Infinity, right?
Infinity + Infinity - Infinity - Infinity
2(Infinity) - (Infinity + Infinity)
Infinity - 2(Infinity)
-(Infinity)
Infinity + Infinity - Infinity - Infinity
2(Infinity) - (Infinity + Infinity)
2(Infinity) - 2(Infinity)
(2-2)(Infinity)
0
And, because multiples of Infinity also equal Infinity, -Infinity = Infinity
So Infinity = 0?
That seems to me to be the same kind of falsity that people reach by saying that 9.999 (continuing on so there're inifinty minus 1 digits after the decimal) is the same thing as 9.9999 (continuing on so ther're an infinite number of digits after the decimal)
Is there some kind of rule for how you can simplify infinite things?
Like with negative radicals, you have to simplify to i form before multiplying the radicals (root(-5)root(-5) = root(5)i x root(5)i = -5, not root(-5)root(-5) = root(25) = 5)
I don't really know that much about math (I just finished Alg.2) yet, but I have more of an interest in it than most people in my class, and if I do choose to teach in the future, it'd probably be in math... but standing up in front of people all day kind of scares me
There are no rules to simplify arithmetic that involves infinity because
you cannot do arithmetic that involves infinity. Quite simply, infinity is not a number. Infinity cannot be expressed as a number or variable, nor can it be manipulated in any way. Indeed, nothing can even
equal infinity. Of course, we get around this by using
limits and saying that a number, x,
approaches infinity.
So...if you desperately wanted to "multiply" infinity by itself, you could just mess around with limits like this:
lim (x-->inf) x^2 = infWhat this is essentially saying is that, when
x approaches infinity,
x^2 approaches infinity. (Note that it is possible to show that
x^2 appraches infinity "faster" than
x does.) This is, of course, mathematically trivial, but it does "prove" that infinty time infinity almost-sorta equals infinity.
I guess my point--if I have one--is that while you technically cannot play around with infinity, you can do the next best thing, if you will, and play around with numbers that approach infinity. In an abstract sense, there really is no difference between my limits and the arithmetic you were doing in your post. Just don't claim that in front of a mathematician!