The Jailbait Wait.

TheConductor

Typically the Equation is meant for teenagers and I notice a few of it are using it to mean that it indicates the ONLY people you can date whereas it's meant to be used to indicate the YOUNGEST, anything older than that is hunkydorey, I should have been clearer.

ClockworkUniverse

^^^Well, the limit is infinity, but at zero, it's less "infinity" and more "the concept of division doesn't make sense at that point."

DYRE

^ One of the limits is infinity.  The other is negative infinity.

ClockworkUniverse

True. But we were talking about ages at first, so I assumed positive numbers ;P

Chagen

There are multiple kinds of infinity? What?

Amazing what we managed to create with only ten basic numbers...

ClockworkUniverse

^The short version of the proof: there are the same number of counting numbers, integers and rational numbers. But there are demonstrably more real numbers than that, so there have to be multiple kinds of infinity. I'll post the long version after the CS test I have in 45 minutes.

inkblot

^^^^^ I was using infinity as a shorthand for "undefined number".

Also, it doesn't really matter if you count by days or minutes. If you're less than a year old, the minimum dating age is 7.

What the fuck are we typing.

Ponicalica

You don't start with only ten basic numbers.  You start with zero and the successor function: that is, the function that takes a number to the number plus one, and is defined by denoting all the rules that apply to it.  This gets you the whole numbers(i.e. nonnegative integers; these are represented by W for whole or N for natural, and may or may not include zero--it depends on the person using them).  From these definitions, you can define mathematical concepts like addition and multiplication--division and subtraction are harder and you don't really have them defined for every number.  The important part, though, is that the whole numbers are the smallest infinite set you can create--for this reason, the number of whole numbers is usually called aleph-null.

Next, you can define the integers(usually represented as Z, which I believe is from a German word) as either a whole number or the negative of a nonzero whole number, and extend mathematical operations to those, and you can even fully define subtraction, which you couldn't do before.  By ordering the numbers 0,1,-1,2,-2,3,-3,4,-4,..., you can map the integers into the whole numbers, therefore, the integers and whole numbers have the same size.  This is important--two sets have the same size if and only if there is an invertible mapping between them.

From the integers, you can define the rational numbers(usually represented as Q, which I think is for «quotient») as a ratio of an integer and a nonzero whole number, and declaring a/b and c/d to be different representations of the same number if and only if ad=bc, and you can define all the usual operations as well as fully defining division.  By running a zigzag path through these, you can map them to the whole numbers as well.  (Actually, the equivalence makes it a little more complicated--I can explain this in a later post)  But the important part is that the rationals are the same size as the whole numbers as well.

Next, we can consider sequences of rational numbers that «converge» in a certain sense(Cauchy sequences deserve their own post as well--for now, just think of decimal numbers like π as the sequence 3,3.1,3.14,3.141,3.1415,...); these become the real numbers, and include numbers such as π and the square root of 2 that are irrational.  Now these numbers are different--if you try to create a sequence of real numbers and map them to the whole numbers in that way, there is no possible way that you can touch every real number, as I can always find a real number you didn't include, using something such as this.  Because of this, it can be said that there are more real numbers than whole numbers, and so the number of real numbers cannot be said to be aleph-zero.

Central Avenue

...Is this IJBM II's first proper math derail?

Chagen

I kept trying to formulate a reply but my head is currently exploding from info overload.

But what I said is right in a way. We started with ten basic numerals: 0,1,2,3,4,5,6,7,8,9. From those we created a massive amount of various mathematics. That's quite amazing to me.

Of course, knowing that math is so much more that it seems, as one could tell from your post, is as amazing.

Vorpy

Infinity + 1 = 0, since infinity is a series of 9's that never end. If you add 1, all the 9's turn to 0's, but since there is no end to put the one, it simply becomes a giant strand of 0s with no value.

Ponicalica

No, Vorpy, the infinite string of 9s that never end is just the 10-adic version of negative one.

Komodin

...Is this IJBM II's first proper math derail?

To my knowledge, yep, and, in my personal opinion, the thread is better off this way. I'd rather talk about the plethora of mathematic concepts than "Aw shucks, I'll have to wait until this underage girl I want to sex with is old enough for me to sex her up legally... or do I?"

Vorpy

Either way, you should be allowed to stick your fingers into a girl regardless of how old she is.

Komodin

... and this thread sucks again. Way to go, Vorpy, you crazy sucka.

Vorpy

+1 Attention.

Thank you Komodin.

DYRE

I'd rather talk about the plethora of mathematic concepts than "Aw shucks, I'll have to wait until this underage girl I want to sex with is old enough for me to sex her up legally... or do I?"

I, on the other hand, would rather talk about anime girls.  Perhaps this is why I'm doing so bad in my Calculus class.

Nyarly

I wholeheartedly agree with Vorpy. Why should only older girls have all the fun? Why should I wait years until I sex my cute little girlfriend, whose age has only a single digit? And why should only Vorpy creep out Komodin?

^ You talk about little girls in Calculus class?

Chagen

No, Vorpy, the infinite string of 9s that never end is just the 10-adic version of negative one.

...I thought negative one was "-1".

Vorpy

-11111111111111111111111111111111111111111111111111+

DYRE

You talk about little girls in Calculus class?

No.
Actually I think I've probably talked about lolis while I was in Calculus class before. Just, on the internet, not to people in my calc class.

Chagen

I'm discussing math and lolis in a biology claas right now.

We're just watching a video and have no work assigned right now, though.

Central Avenue

I, for one, welcome our new loli overlords.

(For some reason DYRE's "I, on the other hand, would rather talk about underage girls" made me think of this)

Chagen

I'd rather talk about shotas dressed like lolis.

Nyarly

I'd rather have ants than lolis as overlords. I don't want to be ruled by lolis, if anything I'd rule over them.

Komodin

I, on the other hand, would rather talk about underage girls.  Perhaps this is why I'm doing so bad in my Calculus class.

Somehow, I knew you'd say that.

Vorpy

Komodin...you are doing it again...

ClockworkUniverse

Aw, Ponicalica beat me to the cardinality infodump... :<