This is something straight out of an xkcd comic where the guy builds a bot to buy random $1 items from a website and he keeps getting things that could put him on an FBI watch list.
I'm not disagreeing with you. Yes, an infinite series can have a finite sum, no argument there but what I am arguing with is that people are saying the ball stops bouncing after time t = whatever. Everyone is confounding two things here, air time and bouncing. Yes, the air time is finite but the bouncing isn't. So you can't say it stops bouncing after time t = whatever if you calculate t = whatever by assuming infinitely many bounces which is what everyone is doing because they are summing a geometric series where the terms of the series represent the air time of each bounce.
This doesn't address the fact you are making a logical fallacy. You can't make a calculation assuming the ball bounces infinitely often and then after the calculation go back and say the ball stops bouncing because it invalidates your original calculation.
I am familiar with Zeno's paradox and all other things Zeno and infinite series summing to finite things but there is fallacy here that nobody seems to get. Yes the time taken is indeed a geometric series but if the time taken is a geometric series, an infinite one at that, then that means there are infinitely many bounces, no? So if there are infinitely many bounces how can you claim the ball stops bouncing? You are confounding two things, air time which is indeed finite because it forms a geometric series, and the number of bounces. You can not have an infinite geometric series to calculate the time and only have finitely many bounces.
Ya, and what are the terms in the series representing? Is it air time of each bounce? Your calculation makes it clear that it is. So you are saying you are calculating the air time for infinitely many bounces, the key word here is infinite, i.e. the ball bounces up and down, up and down infinitely often. So if the ball bounces infinitely often how can it stop and roll on the floor because infinitely many bounces means not stopping after finitely many bounces and rolling on the floor. Your calculation for the time is confounding two things, air time and bouncing. You can calculate the air time assuming infinitely many bounces but then you can't go and claim that the ball stops bouncing after t = whatever because you calculated t = whatever assuming the ball never stopped bouncing and then after the calculation went back and changed your assumption, that is a logical fallacy if I ever saw one.
Same mistake as everyone else. Geometric series means infinitely many bounces and infinitely many bounces means it never stops bouncing. Everyone is making the same logical fallacy.
No, you are making the same mistake as some of the other people. You are summing a geometric series so you are saying the ball bounces infinitely often and the time it takes for the ball to bounce infinitely often is blah. But if it bounces infinitely often then it never stops to roll on the floor because if it did stop and roll on the floor in a finite amount of time then you wouldn't have an infinite series to sum which would mean that the potential energy in the horizontal direction would be zero in a finitely many bounces which contradicts the problem statement and part of your original reasoning.
True but then in what order are you calculating things. In order to have an infinite series for the air time to sum you must assume there are infinitely many jumps so if there are infinitely many jumps then the ball never rolls on the floor by definition. But then if you say you sum the infinite series of time intervals and the ball stops at that time then you don't have infinitely many bounces because if there were infinitely many bounces the ball would not roll on the floor. So you are missing something somewhere.
Ah but it takes infinite amount of time for the ball to stop and start rolling on the floor and infinite amount of time means the ball bounces infinitely often so the ball never stops to bounce and never rolls along the ground. It is easy to calculate how long the ball stays in the air on each bounce a formula from high school physics tells you that the potential energy of an object is m x g x h so if you know the potential energy then you know how high the ball is and if you know how high the ball is then you know how long it will take for it to fall to the ground but no matter how long you wait the ball will have some potential energy left so it will be bouncing no matter how long you wait.
It's true that the horizontal energy doesn't change and it keeps going to the right but it stays in the air for less and less on each bounce and travels a shorter and shorter distance on each bounce assuming the ball only goes forward when it bounces but you still didn't answer the question because if you sum the total time the ball will spend in the air you will get a finite number so the ball will travel a finite distance which is a much better description of what happens to the ball than just saying it keeps going to the right.
So I did some math starting with 100J of potential energy and summed a geometric series to see how long it would stay in the air if we had infinite time to sum the geometric series and it was some finite number. Then I assumed the initial velocity in the horizontal direction was 1 m/s so if we had infinite time the ball would travel some finite distance because it would bounce infinitely often and in every such bounce it would be in the air some amount of time and would travel at a speed of 1 m/s in that amount of time. But this assumes that the ball doesn't roll along the floor when it comes down and immediately bounces up as soon as it hits the floor which is unrealistic because it means I'm assuming infinite impulse on each bounce because the momentum of the ball changes and I'm assuming this takes 0 seconds. So the best I was able to do was give an upper bound on the total distance the ball would travel if the universe were to last forever. It's a lot like Zeno's arrow or is it Achilles and the tortoise.
so other activities (non-chronologically) were things like writing operating system components, replacing parts of the java collections framework with probabilistic data structures or building our own red/black trees, designing chips, writing an embedded system or microkernel, creating oCaml/scheme/haskell parsers and REPL's, building C++ as stroustrup first did (by doing lots of plumbing with void pointers in c), designing new DSL's, spending hours on theory of computation proofs and decidability, implementing the viterbi algorithm for a speech recognition system and other wondrous dynamic programming problems, binary and stereo vision, distributed/parallel computing, and the list goes on...
All that can be found in good books and without a blabbering blowhard in front of a blackboard.
I'm not favoring dumbing down curricula. I'm favoring honest practices on the part of the administration to not overcrowd their graduate departments simply because they have too many lower division class offerings and somebody has to be a TA for those classes. It's unfair to everyone involved and the university is the only one that benefits because they pocket the tuition fees.
My point is that math professors as a bunch put up with this kind of stuff all the time because more than half of the incoming class is just going to be horribly unprepared for any kind of graduate work. Are the students to blame for being unprepared? Yes, I think so but there is also the fact that universities take on way too many graduate students simply because somebody has to be a TA for all the lower division classes the math department offers. This is just bureaucratic bloat and a byproduct of this bureaucratic bloat is that people who shouldn't get a PhD get pushed through the system because it keeps the attrition rate down, at least on paper. So it's great that this guy is standing up for what he believes in but the problem is more systemic and I doubt his one man stand against one student is going to make much difference to how the universities currently operate.
The way universities are pumping out PhDs it's not surprising that a whole bunch of requirement are simply being swept under the rug. Universities figured out a long time ago that graduate students are basically slave labor and they accept way too many students that fumble their way through the program without really accomplishing anything. So get off your high horse and put the blame where it should be placed.
There must be something else at stake here. This kind of thing happens all the time and now all of a sudden some professor decides to stand up. This is definitely not the full story.