Aqua-Soft ForumsMy life is more pathetic than your life.
I am confused on how we got to discussing infinity and dividing by zero. Though, it is a neat little discussion.
Well it is pi-day ... 
I don't think I am fully grasping the logic behind alephs. What separates an aleph 1 from an aleph 2 and so on?
I'm not sure if this is what Stevie is referring to, but if you think about it, there has to be seperate levels of infinity. Like between 0 and 1 there are infinite numbers. But are there more numbers between 0 and 1 than between 0 and 2? Twice as much? 2*infinity? Is 2*infinity greater than infinity? Why is Unbe a **** killer 
? Such are the un answered questions of mathematics!
Feel free to correct me if I'm wrong guys, but we can take this to another level...:What's more, there are an infinite number of positive integers. As such, we can reason that there must be an infinite number of potential values between 0 and 1. This, then, means that there are an infinite number of infinities between 0 and infinity. This, if I remember correctly, is what is mathematically known as "aleph 1" infinity (with a single level of infinity being "aleph 0").
If I remember correctly, there are up to 3 or 4 levels of aleph, which start to involve things like complex (imaginary) numbers.
This lesson was brought to you by the numbers i, e, π, and ∞.
that is correct. the lowest level of infinity (aleph 0) is the set of natural numbers. between 0 and 1 are infinitely many numbers, but this infinity is greater than the set of all natural numbers. cantor offered his diagonal argument to prove this, but we shall not go into it here. the thrust of the proof is that there is no one-to-one correspondence (i.e. a bijection) between the two sets.
another example of a higher order infinity can be constructed with power sets.
that is correct. the lowest level of infinity (aleph 0) is the set of natural numbers. between 0 and 1 are infinitely many numbers, but this infinity is greater than the set of all natural numbers. cantor offered his diagonal argument to prove this, but we shall not go into it here. the thrust of the proof is that there is no one-to-one correspondence (i.e. a bijection) between the two sets.another example of a higher order infinity can be constructed with power sets.
Cantor's diagonal argument! That's the bloody thing I was trying to think of all night last night after posting here!
Isn't Maths fun? 
http://planetmath.org/encyclopedia/Cantors...alArgument.html
http://en.wikipedia.org/wiki/Cantor's_diagonal_argument
Maybe you guys could like to read these?
oooooo math is so much fun you know. especially studing euler's stuff. that's why i want to be just like him!
but, that statement for me is wrong. it is debateable. so you aren't wrong. i just disagree. infinity means any number that extends forever. any real number. right? and if you multiply each side by 0 you will get x = infinity * 0. nothing multiplied by 0 can equal to anything other than 0.
what level of education does an american need to have in order to engage in a discussion like this one? if it's high-school then i think we just broke a few myths about american education system.
meh, engaging in such conversations online is really not that hard - no myths have been broken here, this is not an accurate normal distributed population
@steelfist: the step taken to divide a number by 0 and then multiply it by 0 doesn't exist.
0/0 is non existent.
a) 0 divided by ANY number is 0
ANY number divided by 0 is infinity
so what is 0/0 ?
its not infinity
lol stevie. you could've asked.
what level of education does an american need to have in order to engage in a discussion like this one? if it's high-school then i think we just broke a few myths about american education system.
the cantor work in transfinite mathematics is college material usually, but i was teaching myself in high school. yes, i'm a math geek.
OK, I am ****ing pissed off right now because I had a good couple of paragraphs explaining it, but then I scrolled down and FireFox crashed. So you are only going to get cliff notes on what I said.what level of education does an american need to have in order to engage in a discussion like this one? if it's high-school then i think we just broke a few myths about american education system.
I got introduced to imaginary numbers in Algebra 2. By College Algebra, you would definitely know about imaginary numbers. It is hard to say at what age you will know this because they generally put people that don't understand it in a lower math class. I would say about half of the people that graduate from High School would have been introduced to imaginary numbers. Would that mean they undertand the concept? Most likely not. Students just learn enough to get an A in the class, not to educate themselves. Because the A is all that matters, right?
@ Seph - I would have to agree. We have a lot of people from Britain, Australia et cetera here. Or at least, it is really the people that understand this would participate. It is much easier to avoid something on the internet and not be known.
class 10 to 12 students in india (14-17) slog their *ss off doing millions of crazy IIT problems every day just to get through the coaching for the exam, let alone the actual exam.
ironically those who get through with top rankins are generally too middle class to
a) afford a computer
or
bother visiting A/S everyday and reading threads like these
0/0 is a non existant number. it's just like solving for square root of x where x is a negative number. even though imaginary numbers helped this square root problem, 0/0 cannot be worked with. also, 0/0 = x is not an equation because multiplied by 0 it will equal to 0 = 0x. so any number will fit, so you cannot detirmine what 0/0 is. it can be one, 0, or any other number. the rules 0/x will always = 0 and x/x = one contradicts in this situation.
also please note that infinity is not a number so it can have relationships with 0/0. so, infinity can equal 0/0, but in which direction? there is -infinity and +infinity and 0/0 = -0/0 so that dosen't perfectlly work.
I'm fairly sure that 1 / 0 DOES NOT equal infinity.
I could find a proof online, but I just want to explain my reasoning.
Okay, let's solve this as basic algebra. You all are old enough for that, right?
1 / 0 = x.
Therefore, 0 x = 1.
What number times 0 equals 1?
We've stated that NO number multiplied by 0 is equal to 1. The correct answer is Undefined.
-NC
P.S: I don't think that even 0 * infinity is 1. After all, you have zero quantities of this "infinity non-number." It's still equal to 0.
that's exactlly one of my points. infinity can never be a number. it's an expression. no number, or fraction can be infinity because it is not a number.
do you guys think that 0 * infinity always 0? i think so
1 / 0 = x.Therefore, 0 x = 1.
You're missing the middle step, where you multiply both sides by zero. This normally works, because then you get
1 * (number/number) = x * number
and number/number = 1.
Does 0/0=1? Not necessarily. Therefore, the basic algebra breaks down.
However, draw a graph of 1/x, as x approaches 0. You'll see, that the graph approaches infinity (never gets there, because that's technically impossible, silly Buzz Lightyear and his "To Inifinty" stuff).
Well, look at what happened when I tried to put 0/0 through the Windows calculator.
Did you know that the population of the universe could be considered 0?
-NC
"We know that there is an infinite number of planets simply because there is an infinite area for
them to be in (see point 1). But not every one of these planets are inhabited, therefore there must
be a finite number of inhabited ones. And since any number divided by zero is as near to nothing
as makes no odds, the population of the entire universe can be said to be zero."
I just recited that from memory. Eat that.
/me walks into the room with a lady by his arms..
*clears throat*
*geeks typing away in their calculators / copy pasting from math sites*
*sees no apparent reaction*
/me twirls and turns the stunning lady in her short dress...
/me walks off seeing the lack of interest
You guys keep it up :confused:
what? us? you insulting math lovers? we are just sharing ideas and insights on numbers.
0/0 is undefined because there are infinite answers to this equation. period. if it does show you the answer, then it will show 1 2 3 4 5 6 7 8 9 and fractions and infinite numbers between 0 and 1 and between 0 and 0.01 and so forth. the equation 0/0 = x cannot be solved, or, can be solved simply as "all numbers"
the equation 0/0 = 1 is logical and can be proven correct. but, 1 is just one number out of infinity that fits in the equation. so it cannot be exactlly as 0/0 = 1 but that does not mean that 0/0 = infinity because it's just like trying to solve an equation and multiplying both sides by 0. it is just a rewrite of one of the rules of infinity. infinity * 0 = 0.
@nc: you can put it as
the limit of 1/x, as x approaches 0, is infinity
i.e. as x tends towards 0 (never really 0), 1/x tends towards infinity (nevery really infinity)
thats how we started off our calculus
Before we continue, let's just all remember this very basic rules that we learned in primary/elementary/grade/whatever-it-is-called-in-your-country math:
1 * 1 = 1
1 * x = x (where x can be any number)
1 * 0 = 0
x * 0 = 0 (where x can be any number)
Here's another question to work your minds out: is (infinity * 1) = (infinity * 2)?
from what i've been taught in high school, you're not even allowed to mention division by zero if you're not talking about limits. if you are, then
lim 1/x = infinity if x approaces zero.
lim 1/x = zero if x approaces infinity
lim x/y if x app. zero and y app. infinity is subject for further investigation 
A.K.R: yes, if it's about limits.