Ya .. I'm sorry, I can't get behind the idea that the sum of an infinite positive numbers with addends that are monotonically increasing with a modulus bigger than 1 adds to -1/12.
I'm not sure if the claim that this sum is negative or finite frightens me more ...
Ha. I know it is kind of crazy. That's part of the fun of math though. I think a lot of people think in terms of basic arithmetic, so even the concept of infinity is understood in a certain way. Maybe my interest in theoretical physics makes me a little too open to these ideas, but it wasn't too long ago (in the scope of human existence) that people didn't even know about infinite series, calculus, or computers. How can we really say that we completely understand infinite series? Ask someone from 2000 years ago what they know about cryptography (if possible of course) and you see what I mean. There is something to it, but what it is, is not yet known.
No. I'm not saying that your claim is crazy. I'm saying that it is flat-out wrong . . .
I even stated why in my response.
There's a lot that we do understand about infinite series, sequences, partial sums, etc.
I suggest a first year graduate course on real analysis.
Okay. I'll concede that I am by no means trying to debate you on the subject, but you do understand that there are some pretty smart people who disagree with you, right? I have a lot of respect for your posts. I think you know a lot about math, but I'm just saying don't cast it aside so quickly. People thought the square root of -1 was wrong logic too, but you see where that went. My field is physics. I need to keep an open mind, because there are some weird things that don't make sense (or are false as you claim) that end up leading to new things that most certainly are not false. Sometimes debating what you hold as truth is where you become the most enlightened.
NOt that im a math guy, but AFAIK, people thought (and still think) that the root of negative one does not exist. And theyre correct.
They use "i" to represent the square root of negative numbers because its useful for figuring certain things out. But that doesnt make it real. Thats why "i" isnt a real number. Its an imaginary number. which is probably why they call it "i".
For example, unicrons aren't real. But the notion of a unicorn in a model might be able to help me solve some sort of problem or answer some sort of question... who knows about what maybe somehting about horse behavior.
THe point is that just because we can represent something thats imaginary and even use that representation to answer a question or solve a problem doesnt mean that suddenly its freaky friday and the rules don't apply anymore.
@theabsolute, I'm sorry. I don't know the people who are disagreeing with me.
It appeared as if I was interacting with someone who had a more innate knowledge about economics than myself and had a legitimate concern about something that I wrote (which, I, admittedly, hold no real knowledge, beyond that of a passing mathematician). You should've seen that at the end of the day (via the course of the dialogue that went on for several hours, if you were following), when we were both able to obtain an agreed upon definition what is money multiplication that we were able to better ascertain the nature of how it is caused.
My initial assumption that it only happens through the lending of deposits, which I conceded to be false in evidence to the contrary, modeled the growth as an infinite geometric series.
Even though my initial assumption was wrong, the same mathematical analysis and model can be applied to fractional reserve banking at large, assuming everything is fixed.
I was presented with a well-laid out real-world example that described the process in such a way that both my intellectual adversary (adversary -- is that the proper word? probably not) agreed.
I understand your field is physics, and you are right that you (or anyone) should keep an open mind.
There is a lot that doesn't make sense. I agree. And intuition can lead one astray.
But if you do the math (and also listen to those who have experience in their disciplines and experts in their field, or don't listen if you do not believe them...) you can tackle the situation with a bit more clarity.
In response to the imaginary number comment ...
Imaginary numbers are a HORRIBLE term.
There is nothing imaginary about the square root of -1. It exists. And is necessary element in what is known as an algebraically closed field.
That is to say, all polynomials (which by definition are finite) which are defined over an algebraically closed field (complex numbers being one such example) have roots in that algebraically closed field. And if one "imaginary" number is a solution, so is its conjugate.
Basically, the complex numbers are a different beast than real numbers, although, under an appropriate isomorphism, R^2 is the same as C.