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Yeah, complex numbers are funny things, you can't really say they exist, but you can't really say that they don't, but, withouth them, lots of things wouldnt be possible. Its surprising the amount of times the complex numbers pop up in real world situations and not just hypotheticals.

I neglected my poor thread last semester, so you all missed out on learning great and wonderful things about groups and subgroups and cosets and such. But this semester im doing heaps good subjects like cryptology, so that will be fun!

Thought id post this picture to get it started again. If you laugh, it means you must be at least a little bit geeky.

God, ive abandoned this thread so much, if this thread for a woman, she would cheated on me about 10 times. But anyway, thought i'd put something here.

Here is a really good example of a Paradox that we learned. For those playing at home, a paradox is something with a no answer, so like; what came first, the chicken or the egg? is a paradox. If i said to you "everything i say is a lie", that's a paradox, because am I lying about lying?

They mess with your head a bit, but it's an interesting mental workout. Here's a really clever one:
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FInd: A NUMBER WHICH CAN NOT BE EXPRESSED IN UNDER TWELVE WORDS

When I say expressed in words, i mean like...
102 can be expressed in words as "One Hundred and Two"
12 can be expressed in words as "A dozen"
2007 can be expressed in words as "The current year"
4 can be expressed in words as "The number of sides on a square"
etc..

So, does this number (which can't be expressed in under 12 words) exist?

Well, numbers are infinite.
But, words are finite (only so many of them).

So, there are only so many sentences that you can possibly make of 12 words or less.
So, there are only so many numbers that you can express in under 12 words or less.

Let's agree that because of this, we definitely CAN find at least one number that can not be described in under twelve words.

BUT!!!

We can describe this number as: "A NUMBER WHICH CAN NOT BE EXPRESSED IN UNDER TWELVE WORDS"

And this sentence is only 11 words long! So, that's to say we CAN'T find this number

CAN we or CANT we?!!!!
This is a paradox

Hello again friends. Now that I work for a gaming company, I'll bet you all will be listening VERY carefully at what I have to say about maths from here on in hehehe. I'm gonna (carefully) do a few posts about gambling to inform everyone here about certain concepts.

The first one I want to talk about is the Gambler's Fallacy:

If i flip a coin 100 times and it lands on heads. What are the odds of it landing on heads next time?





If you said anything but 1 in 2 (or 50% or 50/50) you were wrong. The past flips DO NOT affect the next flip.

You may be thinking...but a tail is DUE.This is wrong. The coin doesn't know how often it has landed on heads. There's no such thing as "catching up". And even if there was, how do you know that before you got there i flipped the coins 1000 times and got a tail every time? The coin does need to eventually have landed on heads the same number of times as tails...but it's got an eternity to do this.

You might look at the situation as a whole and say, well the odds of getting 100 heads is pretty small and 101 would be ever smaller. The more and more heads that come up, the more and more unlikely the situation is.

But think of it this way. The odds of:
H,H,H,H,...H,H,H
is the same is
H,H,H,H,...H,H,T
Because the odds of a head is the same as the odds of a tail. So even by looking it as a whole, it's still the same probability. Sure you might be in an extremely unlikely situation because of what's happened, but unfortunately...there's no escaping it.

You see people in roulette marking down the previous numbers or the number of reds or blacks. Why would casinos LET you take notes in Roulette or other games of chance like this. Do you think they really want to help you? No! It's because they know it wont make a difference. You don't see them giving out pens and papers at the Black Jack table to you?

So, how can you avoid the Gambler's Fallacy?

The best advice I can give you about ANY gambling is to NEVER change your bet. I'll talk a bit more about that next time. But, think of it this way. Imagine being blindfolded, throwing darts at random trying to hit a target. Now...imagine that target moving all the time.