0.9... = 1

I'd like to interject here with something I've been thinking about for awhile.  Could it be possible that zero is infinite since it is infinitely smaller than the smallest number?  Zero is complete absence of whatever and a complete absence of something is a whole lot of nothing, if you catch my drift.

zero is a famous infinite limit, constant/x
it is limit as a denomiator gets larger and larger.

How can infinity be greater than infinity? It's not even a number, really...

Some infinities can be "greater than" others.  First we must be clear on what we mean when we say two infinities are equal: two infinitely large sets are the same size if you can pair off all the elements of one set with exactly one element of the other, so that no element in either set is every paired off more than once, and so that no elements in either set are left unpaired.  This is a one-to-one correpondence.

It is the way in which, for example, the set of primes and the set of positive integers have the same size: if you write out all the primes in order, and pair the lowest one with "1", the next lowest with "2", etc., you eventually have a pairing like I've described above: you have a one-to-one correspondence.

Not all infinitely large sets can be paired off with one another in this fashion.  One of the easiest-to-show examples of this is that there are more real numbers in the interval (0,1) then there are integers (proof emitted due to headache).

It is in this sense of "infinity" and of "greater than" that fathomak's question is fully well-posed.

On the other hand, the senses of "infinity" and "greater than" as used in the following post

One infinity can be greater than another, comparitive in the rate that the two infinities rise.

for example, lim as x->infinity (x) is simply infinity, but lim as x-infinity (2x^2) reaches infinity faster, so it is said to be greater.

are never used by mathematicians.  Instead they say that the first function is O(the second function), or that the rate of divergence of the second is greater than the rate of divergence of the first.  They never "compare infinities" in this fashion.

Quote from: "fathomak"

QED

When are you actually going to get around to doing that?

No, silly, it means "quantum electrodynamics."  In any case, you might want to try scrolling up from your last post.

I'd like to interject here with something I've been thinking about for awhile.  Could it be possible that zero is infinite since it is infinitely smaller than the smallest number?  Zero is complete absence of whatever and a complete absence of something is a whole lot of nothing, if you catch my drift.

This is correct except that zero is not "infinitely smaller" than anything; in terms of absolute value, zero is the smallest number, and there is no smallest number in the set of all numbers greater than zero.

Thanks, Erasmus.  You answered my question very well.

So much for trying to keep it in layman terms, considering if they were mathematicians, this wouldnt be an issue.

What is the square root of i?

What is the square root of i?

That's easy.  It's obviously (1 + i) / sqrt(2).  You get it by finding any complex number whose argument is half that of i, and then normalizing it.

An even easier answer is of course e^(pi/4).

Darn.

Quote from: "fathomak"

What is the square root of i?

That's easy.  It's obviously (1 + i) / sqrt(2).  You get it by finding any complex number whose argument is half that of i, and then normalizing it.

An even easier answer is of course e^(pi/4).

I've got a brainbuster for you Erasmus
What is d/dx of E^x
 :wink:

This is the most retarded argument ever.

Simply because you can't understand it doesn't make it retarded.

Besides, the word retarded is a fundamentally wrong insult. Retarded comes from "mentally retarded", which means to be held back mentally.

So, the argument's being held back? Well, stop holding the fucking dam already!

I've got a brainbuster for you Erasmus
What is d/dx of E^x :wink:

Well, I'm not sure what you mean by "E" so I'll just assume it to be an arbitray constant, and reserve "e" to be that number such that d/dx (e^x) = e^x.

ln E^x = x ln E, which means E^x = e^(x ln E).  Therefore d/dx (E^x) = d/dx (e^(x ln E)), which equals e^(x ln E) ln E, which equals E^x ln E... so that your answer.

If you meant for E = e (maybe you didn't; I don't like to presume), then ln E = 1, and the result simplifies to E^x.

p.s. I may also have been hasty in assuming that E is a constant; perhaps its value depends on x.  In that case, the most general answer comes from the multivariate chain rule and is: E^x ln E + xE^(x-1) * dE/dx.

Simply because you can't understand it doesn't make it retarded.

You think I don't understand? If I cared enough I could be included in this debate. But this is an argument for nerds, I could care less about 0.9999999999 equaling 1. KTHXBAI

If I cared enough I could be included in this debate.

If what you're saying is, "I don't want to contribute to the productive outcome of this thread", then I'd be more than happy to delete all your posts that appear in it.

I'd be more than happy to spam this website enough to bring it down, also. But am I doing so? No.

...But this is an argument for nerds

Yes, if only we could talk about more substantial things like women and myspace, this topic would be so much cooler.

I'd be more than happy to spam this website enough to bring it down, also. But am I doing so? No.

I doubt you'd come close.

EDIT: DOUBLE POST'D

I'd be more than happy to spam this website enough to bring it down, also. But am I doing so? No.

Don't you realize that that makes you a bad person?

Anyway, more nerd talk plz!

Well then we need a new question.  Any good ones?

Quote

...But this is an argument for nerds

Yes, if only we could talk about more substantial things like women and myspace, this topic would be so much cooler.

Myspace sucks, it's for idiots, and women isn't something you discuss, unless it's in-person.

EDIT: Here's a topic to discuss. How much of pi can you memorize?

Well then we need a new question.  Any good ones?

What does "dimensionality" mean?

ill use my simple mind to say that 1/3 +2/3 = 3/3 = 1

there, problem solved  

Myspace sucks, it's for idiots...

Let's not assume personal opinion to be absolute truth, and make overgeneralizations about myspace users... I personally don't care for myspace.

Quote from: "BOGWarrior89"

I'm saying there is no way to check our answers.  Life is all about uncertainty.

It is true you cannot prove causality.  But you can get what seems to be ridiculously close.

In statistics there is a law called "The Law of Large Numbers".  Despite how interesting and action-packed this mathematical theorem is, it relates to the relationship of sample size to the outcome.  The larger the sample, the closer the outcome reflects the truth.  Of course, this is just statistics.

Hume's famous anecdote reguarding this was the room.  Could you prove conclusively that the next time you come to the room it will still be there?  What about if you came and left 999 times, would it be there the 1,000th?

But there is some point where we accept 99% certainty.  Otherwise our abstract world would be too chaotic to function in.

There is no such thing as 100% certainty.

Quote from: "BOGWarrior89"

The process is endless, so you never fully divide one by three.

Problem here: numbers aren't processes.

Problem in your argument: division is a process.

There is no such thing as 100% certainty.

Are you 100% certain?

Quote from: "BOGWarrior89"

I'm saying there is no way to check our answers. Life is all about uncertainty.

You need to study epistemology.  We can check our answers within a given methodology.

No, you can't.  You only think you can.

Quote from: "fathomak"

Well then we need a new question.  Any good ones?

What does "dimensionality" mean?

I attended a very interesting talk on the dimensions of individual points in euclidean space. The speaker proposed an alternative definition for the dimension of a point, and then proved that for "nice" fractals (which includes almost every example you're likely to see), the (hausdorff) dimension of the fractal is the supremum of the dimensions of the points in the fractal. Which is at the same time complete nonsense and yet surprising an interesting, and perhaps has some merit after all.

Anyways, this leads me to believe that "dimensionality" means "dimension", but "dimension" can mean whatever the hell you want it to mean.

Well, here's the answer (I think) to my previous question:

Quote from: "fathomak"

Which is larger, the set of all positive real integers or the set of all primes?

[Hand-wavy explanation that my lab TA gave me]

Ok, well, now look at each set on an interval, like (0,10), and understand that the larger the number, the harder it is to find a prime number, and therefore, the set of positive intergers is bigger.