Okay, I'm confused on something that's probably rather basic but it's really annoying me so a little help would be appreciated.
I'm reading a book and it's going over how the Golden Key was arrived at by basically using the Sieve of Eratosthenes on the Riemann Zeta Function.
And it gets to this point
Then you multiply both sides by the fist expression and subtract the new expression by the first expression and you end up hypothetically with something like:
Well heres the part that just isnt computing to me, its saying that the next step that was taken was dividing the left side by the right side, fair enough if it ended up being ζ(s)=1/(the entire term that was on the left).
Instead, it says that after dividing the left side by the right side we end up with:
This makes absolutely no sense to me, and I tried working it out myself by doing this:
(1/2)(1/2)(1/2) = a; where a obviously is equal to 1/8
and if you divide how it shows to divide, you end up with:
And this obviously isnt right, so could someone please explain how this was arrived at correctly?
The way I look at it is like this, much like when you are working in algebra, if you do something to one side of an equation you have to do it to the other side of an equation for it to still be equal.
Well, like that, if we are working only on one side of an equation, if we do something to that side of the equation we have to do the opposite or inverse of that action for that side of the equation to still hold true. Simple example: if our equation was 5+5=10
If we decided to subtract 3 from the first side we'd get 5+5-3=10, well that's not true , but as long as we did the opposite of that our equation would still be true. 5+5-3+3=10, now it's true again.
Same goes for with the fractions, in essence when looking atAll we are doing is dividing that entire side of the equation, and at the same time multiplying the entire side of the equation by 4. Like this:
With what you are trying to do, you are dividing the same side of the equation by 8, twice. Going back to my simple example, 5+5=10, your action would look something like this, 5+5-3-3=10. And that just can't work, if you do something to a side, you have to do the opposite to keep the equation equal.
So, what you did would look like this:
And that equation is definitely not the same as
Okay, maybe it was easier than I thought to simplify, I think I figured it out. I just wasn't sure if I should distribute first or FOIL first. And what I ended up with was this:
And it seems like you can divide, which seems weird, but it comes out with the right answer.
So, it seems that I can divide like that, and I simplified correctly?
Now that's interesting, when I was trying to work out a formula that didn't involve a recurrence, I actually worked out these first two patterns and were trying to figure a way to use them both, but ultimately couldn't.
And actually, I don't remember what I had done, but I had come to a pattern that went up by 4 constantly. I was working on the computer though and didn't save my notes.
It would seem that my structure in my assertion was wrong, throwing off data. More correct is my conclusion is: "that joining this forum is a Nash Equilibrium."
And here are my assumptions given my estimated values of what joining would have on our species as a whole.
| | |
| 5 | 1|
| | |
Joining | | |
| 3 | 1|
Not | | |
| | |
Joining, from my calculation(maybe I have overestimated what the values truly are) Joining is in one's best interest as advancements in mathematics can only go to bettering the human species as a whole; mathematics, in my humble opinion, is the building blocks to life.
I know that I'm capable, it's just that I'm 24 almost 25, and I haven't taken any math since I was 16 and even then in High School I never applied myself. It's a shame really, because now I'm in college and I'm taking college Algebra, which is almost sad really. I just feel like I'm really far behind, and I'm really not sure how to go about catching up quickly.
I understand, this information is still very helpful to me. It's obviously showing me there is a lot I need to learn; I'm a freshman in college and I really want major in mathematics, but from your general knowledge and understanding it would seem that I'm extremely far behind and I'm not sure I can catch up. So, this helps a bit...