@pingOfDoom Apart from what the others said, that is surely not all it says. For example it probably defines the function more precisely than you have so far
By the way, what is it like to be a mathematician/professor/researcher ? Are you happy with your choice @TedShifrin ? I'm just wondering please excuse my curiosity.
Most of us, I think, find it a rewarding career. Some are in it just for research, some just for teaching, and a lot for a blend. But mostly we're doing something we enjoy doing and find fulfilling. Not sure how many people in other careers feel that way.
We recently got into the basics of Set Theory (The course wasn't really named that), and after a few minutes I realized that they were absolutely no numbers on the board, can we consider in the case Sets being the mathematical object of the study ?
I like it ! @TedShifrin It makes the ability to generalize facts and apply math pretty much everywhere, I don't consider abstraction bad, it makes you feel the purity of math.
@Mahmoud Indeed, abstraction is one of the great strengths of math, in that it can sometimes remove unnecessary details that were not needed for the desired conclusions
I recall laughing when I saw the first few proofs, I think in calculus where they did few algebraic tricks. It was how it transformed such complex things into such simple 'magic tricks'...
What still fascinates me is the axioms, we don't have to check every single one of the infinite cases, after setting the corresponding rules of the game.
@TedShifrin It's is a great honor for us humans, as finite creatures, to put our hands on those incredible facts and grasp them, arriving at Infinite results, in a finite world.
I don't mean to be a stickler, I'm sorry if it came out that way, it's just I'm ocd sometimes
*It's a great honor for us as humans, as finite creatures, to put our hands on those incredible facts and grasp them, arriving at infinite results in a finite world
But yeah I really do agree it is very divine for us to be able to use infinity - something that can never exist - to arrive at conclusions that very much exist.
@Î›ÎµÎ³Î¯Ï‰Î½ÎœÎ¬Î¼Î¼Î±Î»Ï ÎŸÎ—Ê¹ most divisions are not defined in peano arithmetic, so why try to define one that cannot be defined even in more general structures?
@TobiasKildetoft I know it's undefined and anything using it becomes unintelligible gibberish, I was just thinking about it in the realm of first-order logic.
@Î›ÎµÎ³Î¯Ï‰Î½ÎœÎ¬Î¼Î¼Î±Î»Ï ÎŸÎ—Ê¹ There is not much to have knowledge about (no idea what GEB is). You cannot divide by zero in any meaningful way and retain a useful structure
There's a program at the Newton center about low-dimensional topology homology theories. I emailed one of the organizers to ask if they have funding for grad students to attend.
@TedShifrin I think I'd just say heres this person's theorem, and here's my theorem see how its an improvement of this person's theorem. Are there more thereoms like these two?
Because you need to have the smallest number that's a multiple of $\pi$ and also a multiple of $2\pi/3$. Periodic with period $a$ also means periodic with period $ka$ for any integer $k$.
Alternatively, if you're more of the programmatic school of thought, think of it like a game of Fizz Buzz and the period is how often you say both Fizz and Buzz.
So, if the first sinusoid is Fizz and you say it every $2$ times, the second sinusoid is Buzz and you say it every $3$ times, then you say FizzBuzz every $\gcd(2, 3) = 6$ times.
I went to the hardware store today looking for an Alan Wrench. Oh my goodness, every product had a metric counterpart, except that the set I was looking for only had a Metric set.
